LMFDB - Embedded newform 100.9.j.b.91.37

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,9,Mod(11,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 8])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.11"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.j (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [464] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$464$
Relative dimension:	$116$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			91.37
Character	$\chi$	$=$	100.91
Dual form			100.9.j.b.11.37

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.73089 - 13.4079i) q^{2} +(-122.140 + 39.6856i) q^{3} +(-103.543 + 234.126i) q^{4} +(139.543 + 609.223i) q^{5} +(1598.49 + 1291.15i) q^{6} -4148.65i q^{7} +(4043.16 - 655.829i) q^{8} +(8035.23 - 5837.94i) q^{9} +(6950.07 - 7190.03i) q^{10} +(-12553.6 + 17278.6i) q^{11} +(3355.32 - 32705.2i) q^{12} +(-29310.4 + 21295.2i) q^{13} +(-55624.6 + 36221.4i) q^{14} +(-41221.1 - 68872.6i) q^{15} +(-44093.6 - 48484.2i) q^{16} +(17111.0 - 52662.1i) q^{17} +(-148429. - 56765.2i) q^{18} +(-185346. - 60222.4i) q^{19} +(-157083. - 30410.4i) q^{20} +(164642. + 506715. i) q^{21} +(341273. + 17460.3i) q^{22} +(-3718.80 + 5118.49i) q^{23} +(-467803. + 240558. i) q^{24} +(-351681. + 170025. i) q^{25} +(541430. + 207064. i) q^{26} +(-254472. + 350251. i) q^{27} +(971305. + 429564. i) q^{28} +(-92269.9 - 283978. i) q^{29} +(-563539. + 1.15401e6i) q^{30} +(-845889. - 274846. i) q^{31} +(-265095. + 1.01451e6i) q^{32} +(847586. - 2.60860e6i) q^{33} +(-855482. + 230365. i) q^{34} +(2.52745e6 - 578914. i) q^{35} +(534817. + 2.48573e6i) q^{36} +(-1.16176e6 + 844066. i) q^{37} +(810776. + 3.01089e6i) q^{38} +(2.73485e6 - 3.76420e6i) q^{39} +(963739. + 2.37167e6i) q^{40} +(-970017. + 704759. i) q^{41} +(5.35651e6 - 6.63157e6i) q^{42} -5.72951e6i q^{43} +(-2.74552e6 - 4.72820e6i) q^{44} +(4.67787e6 + 4.08061e6i) q^{45} +(101097. + 5172.32i) q^{46} +(357755. - 116241. i) q^{47} +(7.30972e6 + 4.17197e6i) q^{48} -1.14465e7 q^{49} +(5.35017e6 + 3.23082e6i) q^{50} +7.11120e6i q^{51} +(-1.95087e6 - 9.06729e6i) q^{52} +(3.48916e6 + 1.07385e7i) q^{53} +(6.91790e6 + 353934. i) q^{54} +(-1.22783e7 - 5.23686e6i) q^{55} +(-2.72080e6 - 1.67736e7i) q^{56} +2.50281e7 q^{57} +(-3.00194e6 + 3.71652e6i) q^{58} +(-223104. - 307076. i) q^{59} +(2.03930e7 - 2.51964e6i) q^{60} +(3.96007e6 + 2.87716e6i) q^{61} +(3.70026e6 + 1.37412e7i) q^{62} +(-2.42195e7 - 3.33353e7i) q^{63} +(1.59170e7 - 5.30324e6i) q^{64} +(-1.70636e7 - 1.48850e7i) q^{65} +(-4.23760e7 + 1.14111e7i) q^{66} +(1.38518e7 + 4.50073e6i) q^{67} +(1.05578e7 + 9.45892e6i) q^{68} +(251083. - 772754. i) q^{69} +(-2.98289e7 - 2.88334e7i) q^{70} +(3.43784e7 - 1.11702e7i) q^{71} +(2.86590e7 - 2.88734e7i) q^{72} +(3.57169e6 + 2.59498e6i) q^{73} +(2.14603e7 + 8.20727e6i) q^{74} +(3.62067e7 - 3.47235e7i) q^{75} +(3.32909e7 - 3.71585e7i) q^{76} +(7.16827e7 + 5.20805e7i) q^{77} +(-7.43477e7 - 3.80378e6i) q^{78} +(-2.97007e7 + 9.65034e6i) q^{79} +(2.33848e7 - 3.36285e7i) q^{80} +(-2.95565e6 + 9.09657e6i) q^{81} +(1.79184e7 + 6.85271e6i) q^{82} +(-1.76996e7 - 5.75094e6i) q^{83} +(-1.35683e8 - 1.39200e7i) q^{84} +(3.44707e7 + 3.07578e6i) q^{85} +(-7.68207e7 + 5.00238e7i) q^{86} +(2.25397e7 + 3.10232e7i) q^{87} +(-3.94244e7 + 7.80930e7i) q^{88} +(4.01599e7 + 2.91778e7i) q^{89} +(1.38704e7 - 9.83476e7i) q^{90} +(8.83465e7 + 1.21598e8i) q^{91} +(-813313. - 1.40065e6i) q^{92} +1.14224e8 q^{93} +(-4.68207e6 - 3.78184e6i) q^{94} +(1.08253e7 - 1.21320e8i) q^{95} +(-7.88295e6 - 1.34433e8i) q^{96} +(-1.94250e7 - 5.97840e7i) q^{97} +(9.99378e7 + 1.53473e8i) q^{98} +2.12125e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 464 q + 29 q^{2} + 509 q^{4} - 1230 q^{5} - 515 q^{6} + 21284 q^{8} + 262434 q^{9} + 3445 q^{10} - 35805 q^{12} - 29522 q^{13} - 33705 q^{14} - 63391 q^{16} - 319922 q^{17} - 569696 q^{18} + 1244935 q^{20}+ \cdots + 209675864 q^{98}+O(q^{100}) $ 464 * q + 29 * q^2 + 509 * q^4 - 1230 * q^5 - 515 * q^6 + 21284 * q^8 + 262434 * q^9 + 3445 * q^10 - 35805 * q^12 - 29522 * q^13 - 33705 * q^14 - 63391 * q^16 - 319922 * q^17 - 569696 * q^18 + 1244935 * q^20 + 39360 * q^21 + 140220 * q^22 + 989900 * q^24 - 431710 * q^25 - 855842 * q^26 - 2358605 * q^28 - 2884562 * q^29 + 7229675 * q^30 - 7078666 * q^32 - 1866570 * q^33 + 1448973 * q^34 + 777029 * q^36 - 7317972 * q^37 + 4012465 * q^38 - 4154830 * q^40 + 1687438 * q^41 - 21337315 * q^42 + 510580 * q^44 + 2596050 * q^45 + 1721385 * q^46 + 41153690 * q^48 - 396068336 * q^49 - 60015715 * q^50 - 8419912 * q^52 + 26717388 * q^53 - 13729145 * q^54 + 7138890 * q^56 - 19745300 * q^57 - 41444182 * q^58 + 96768050 * q^60 + 26136558 * q^61 - 87505940 * q^62 + 19616924 * q^64 + 22030140 * q^65 - 69968200 * q^66 + 276958 * q^68 - 73697610 * q^69 + 39639840 * q^70 - 145994351 * q^72 - 39004722 * q^73 + 4922908 * q^74 - 19181080 * q^76 + 111211200 * q^77 - 197089615 * q^78 - 395680960 * q^80 - 539852286 * q^81 + 186999258 * q^82 - 377672700 * q^84 - 283475540 * q^85 - 340843785 * q^86 - 29231040 * q^88 - 206040612 * q^89 + 351285695 * q^90 + 43044280 * q^92 + 241823660 * q^93 - 442380075 * q^94 - 474931550 * q^96 + 2388718 * q^97 + 209675864 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$e\left(\frac{1}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−8.73089	−	13.4079i	−0.545681	−	0.837993i
$2$	−8.73089	−	13.4079i	−0.545681	−	0.837993i
$3$	−122.140	+	39.6856i	−1.50790	+	0.489946i	−0.942310	−	0.334741i	$-0.891351\pi$
$3$	−122.140	+	39.6856i	−1.50790	+	0.489946i	−0.565589	+	0.824687i	$0.691351\pi$
$4$	−103.543	+	234.126i	−0.404466	+	0.914553i
$5$	139.543	+	609.223i	0.223268	+	0.974757i
$5$	139.543	+	609.223i	0.223268	+	0.974757i
$6$	1598.49	+	1291.15i	1.23340	+	0.996256i
$7$		−	4148.65i		−	1.72788i	−0.503592	−	0.863941i	$-0.667989\pi$
$7$		−	4148.65i		−	1.72788i	0.503592	−	0.863941i	$-0.332011\pi$
$8$	4043.16	−	655.829i	0.987098	−	0.160114i
$9$	8035.23	−	5837.94i	1.22470	−	0.889794i
$10$	6950.07	−	7190.03i	0.695007	−	0.719003i
$11$	−12553.6	+	17278.6i	−0.857429	+	1.18015i	0.124747	+	0.992189i	$0.460188\pi$
$11$	−12553.6	+	17278.6i	−0.857429	+	1.18015i	−0.982176	+	0.187961i	$0.939812\pi$
$12$	3355.32	−	32705.2i	0.161811	−	1.57722i
$13$	−29310.4	+	21295.2i	−1.02624	+	0.745606i	−0.967552	−	0.252671i	$-0.918691\pi$
$13$	−29310.4	+	21295.2i	−1.02624	+	0.745606i	−0.0586860	+	0.998276i	$0.518691\pi$
$14$	−55624.6	+	36221.4i	−1.44795	+	0.942872i
$15$	−41221.1	−	68872.6i	−0.814245	−	1.36045i
$16$	−44093.6	−	48484.2i	−0.672815	−	0.739811i
$17$	17111.0	−	52662.1i	0.204870	−	0.630525i	−0.794849	−	0.606808i	$-0.792450\pi$
$17$	17111.0	−	52662.1i	0.204870	−	0.630525i	0.999719	−	0.0237175i	$-0.00755024\pi$
$18$	−148429.	−	56765.2i	−1.41393	−	0.540744i
$19$	−185346.	−	60222.4i	−1.42222	−	0.462108i	−0.505916	−	0.862583i	$-0.668845\pi$
$19$	−185346.	−	60222.4i	−1.42222	−	0.462108i	−0.916308	+	0.400474i	$0.868845\pi$
$20$	−157083.	−	30410.4i	−0.981772	−	0.190065i
$21$	164642.	+	506715.i	0.846570	+	2.60547i
$22$	341273.	+	17460.3i	1.45684	+	0.0745350i
$23$	−3718.80	+	5118.49i	−0.0132890	+	0.0182907i	−0.815610	−	0.578602i	$-0.803598\pi$
$23$	−3718.80	+	5118.49i	−0.0132890	+	0.0182907i	0.802321	+	0.596893i	$0.203598\pi$
$24$	−467803.	+	240558.i	−1.41000	+	0.725062i
$25$	−351681.	+	170025.i	−0.900302	+	0.435265i
$26$	541430.	+	207064.i	1.18481	+	0.453118i
$27$	−254472.	+	350251.i	−0.478835	+	0.659059i
$28$	971305.	+	429564.i	1.58024	+	0.698869i
$29$	−92269.9	−	283978.i	−0.130457	−	0.401506i	0.864399	−	0.502807i	$-0.167699\pi$
$29$	−92269.9	−	283978.i	−0.130457	−	0.401506i	−0.994856	+	0.101301i	$0.967699\pi$
$30$	−563539.	+	1.15401e6i	−0.695727	+	1.42470i
$31$	−845889.	−	274846.i	−0.915939	−	0.297607i	−0.187139	−	0.982333i	$-0.559922\pi$
$31$	−845889.	−	274846.i	−0.915939	−	0.297607i	−0.728800	+	0.684727i	$0.759922\pi$
$32$	−265095.	+	1.01451e6i	−0.252814	+	0.967515i
$33$	847586.	−	2.60860e6i	0.714707	−	2.19964i
$34$	−855482.	+	230365.i	−0.640170	+	0.172386i
$35$	2.52745e6	−	578914.i	1.68427	−	0.385782i
$36$	534817.	+	2.48573e6i	0.318416	+	1.47994i
$37$	−1.16176e6	+	844066.i	−0.619881	+	0.450370i	−0.852880	−	0.522107i	$-0.825146\pi$
$37$	−1.16176e6	+	844066.i	−0.619881	+	0.450370i	0.232999	+	0.972477i	$0.425146\pi$
$38$	810776.	+	3.01089e6i	0.388836	+	1.44398i
$39$	2.73485e6	−	3.76420e6i	1.18216	−	1.62710i
$40$	963739.	+	2.37167e6i	0.376461	+	0.926433i
$41$	−970017.	+	704759.i	−0.343276	+	0.249405i	−0.746043	−	0.665898i	$-0.768049\pi$
$41$	−970017.	+	704759.i	−0.343276	+	0.249405i	0.402767	+	0.915303i	$0.368049\pi$
$42$	5.35651e6	−	6.63157e6i	1.72141	−	2.13118i
$43$		−	5.72951e6i		−	1.67588i	−0.545759	−	0.837942i	$-0.683759\pi$
$43$		−	5.72951e6i		−	1.67588i	0.545759	−	0.837942i	$-0.316241\pi$
$44$	−2.74552e6	−	4.72820e6i	−0.732509	−	1.26149i
$45$	4.67787e6	+	4.08061e6i	1.14077	+	0.995119i
$46$	101097.	+	5172.32i	0.0225790	+	0.00115519i
$47$	357755.	−	116241.i	0.0733151	−	0.0238215i	−0.272130	−	0.962261i	$-0.587728\pi$
$47$	357755.	−	116241.i	0.0733151	−	0.0238215i	0.345445	+	0.938439i	$0.387728\pi$
$48$	7.30972e6	+	4.17197e6i	1.37701	+	0.785917i
$49$	−1.14465e7			−1.98558
$50$	5.35017e6	+	3.23082e6i	0.856027	+	0.516932i
$51$			7.11120e6i			1.05114i
$52$	−1.95087e6	−	9.06729e6i	−0.266818	−	1.24012i
$53$	3.48916e6	+	1.07385e7i	0.442199	+	1.36095i	0.885527	+	0.464588i	$0.153798\pi$
$53$	3.48916e6	+	1.07385e7i	0.442199	+	1.36095i	−0.443328	+	0.896359i	$0.646202\pi$
$54$	6.91790e6	+	353934.i	0.813578	+	0.0416244i
$55$	−1.22783e7	−	5.23686e6i	−1.34180	−	0.572295i
$56$	−2.72080e6	−	1.67736e7i	−0.276659	−	1.70559i
$57$	2.50281e7			2.37098
$58$	−3.00194e6	+	3.71652e6i	−0.265271	+	0.328416i
$59$	−223104.	−	307076.i	−0.0184119	−	0.0253418i	0.799712	−	0.600384i	$-0.204986\pi$
$59$	−223104.	−	307076.i	−0.0184119	−	0.0253418i	−0.818124	+	0.575042i	$0.804986\pi$
$60$	2.03930e7	−	2.51964e6i	1.57353	−	0.194417i
$61$	3.96007e6	+	2.87716e6i	0.286011	+	0.207799i	0.721535	−	0.692378i	$-0.243437\pi$
$61$	3.96007e6	+	2.87716e6i	0.286011	+	0.207799i	−0.435524	+	0.900177i	$0.643437\pi$
$62$	3.70026e6	+	1.37412e7i	0.250418	+	0.929949i
$63$	−2.42195e7	−	3.33353e7i	−1.53746	−	2.11613i
$64$	1.59170e7	−	5.30324e6i	0.948727	−	0.316097i
$65$	−1.70636e7	−	1.48850e7i	−0.955911	−	0.833863i
$66$	−4.23760e7	+	1.14111e7i	−2.23329	+	0.601382i
$67$	1.38518e7	+	4.50073e6i	0.687397	+	0.223349i	0.631831	−	0.775106i	$-0.282304\pi$
$67$	1.38518e7	+	4.50073e6i	0.687397	+	0.223349i	0.0555659	+	0.998455i	$0.482304\pi$
$68$	1.05578e7	+	9.45892e6i	0.493786	+	0.442390i
$69$	251083.	−	772754.i	0.0110770	−	0.0340914i
$70$	−2.98289e7	−	2.88334e7i	−1.24235	−	1.20089i
$71$	3.43784e7	−	1.11702e7i	1.35286	−	0.439570i	0.459204	−	0.888331i	$-0.348135\pi$
$71$	3.43784e7	−	1.11702e7i	1.35286	−	0.439570i	0.893652	+	0.448761i	$0.148135\pi$
$72$	2.86590e7	−	2.88734e7i	1.06643	−	1.07441i
$73$	3.57169e6	+	2.59498e6i	0.125771	+	0.0913783i	0.648893	−	0.760880i	$-0.275232\pi$
$73$	3.57169e6	+	2.59498e6i	0.125771	+	0.0913783i	−0.523121	+	0.852258i	$0.675232\pi$
$74$	2.14603e7	+	8.20727e6i	0.715664	+	0.273698i
$75$	3.62067e7	−	3.47235e7i	1.14431	−	1.09744i
$76$	3.32909e7	−	3.71585e7i	0.997863	−	1.11379i
$77$	7.16827e7	+	5.20805e7i	2.03916	+	1.48154i
$78$	−7.43477e7	−	3.80378e6i	−2.00858	−	0.102763i
$79$	−2.97007e7	+	9.65034e6i	−0.762533	+	0.247762i	−0.664365	−	0.747408i	$-0.731298\pi$
$79$	−2.97007e7	+	9.65034e6i	−0.762533	+	0.247762i	−0.0981673	+	0.995170i	$0.531298\pi$
$80$	2.33848e7	−	3.36285e7i	0.570917	−	0.821008i
$81$	−2.95565e6	+	9.09657e6i	−0.0686615	+	0.211319i
$82$	1.79184e7	+	6.85271e6i	0.396319	+	0.151568i
$83$	−1.76996e7	−	5.75094e6i	−0.372950	−	0.121179i	0.116544	−	0.993186i	$-0.462818\pi$
$83$	−1.76996e7	−	5.75094e6i	−0.372950	−	0.121179i	−0.489494	+	0.872007i	$0.662818\pi$
$84$	−1.35683e8	−	1.39200e7i	−2.72525	−	0.279591i
$85$	3.44707e7	+	3.07578e6i	0.660350	+	0.0589222i
$86$	−7.68207e7	+	5.00238e7i	−1.40438	+	0.914497i
$87$	2.25397e7	+	3.10232e7i	0.393433	+	0.541514i
$88$	−3.94244e7	+	7.80930e7i	−0.657408	+	1.30221i
$89$	4.01599e7	+	2.91778e7i	0.640077	+	0.465043i	0.859877	−	0.510502i	$-0.170540\pi$
$89$	4.01599e7	+	2.91778e7i	0.640077	+	0.465043i	−0.219800	+	0.975545i	$0.570540\pi$
$90$	1.38704e7	−	9.83476e7i	0.211407	−	1.49897i
$91$	8.83465e7	+	1.21598e8i	1.28832	+	1.77322i
$92$	−813313.	−	1.40065e6i	−0.0113529	−	0.0195514i
$93$	1.14224e8			1.52696
$94$	−4.68207e6	−	3.78184e6i	−0.0599689	−	0.0484387i
$95$	1.08253e7	−	1.21320e8i	0.132906	−	1.48950i
$96$	−7.88295e6	−	1.34433e8i	−0.0928120	−	1.58278i
$97$	−1.94250e7	−	5.97840e7i	−0.219419	−	0.675302i	−0.998810	−	0.0487645i	$-0.984472\pi$
$97$	−1.94250e7	−	5.97840e7i	−0.219419	−	0.675302i	0.779391	−	0.626537i	$-0.215528\pi$
$98$	9.99378e7	+	1.53473e8i	1.08349	+	1.66390i
$99$			2.12125e8i			2.20826i
$100$	−3.39315e6	−	9.99424e7i	−0.0339315	−	0.999424i
$101$	6.77727e7			0.651282			0.325641	−	0.945493i	$-0.394420\pi$
$101$	6.77727e7			0.651282			0.325641	+	0.945493i	$0.394420\pi$
$102$	9.53462e7	−	6.20871e7i	0.880852	−	0.573589i
$103$	5.30221e7	−	1.72279e7i	0.471094	−	0.153068i	−0.0638424	−	0.997960i	$-0.520336\pi$
$103$	5.30221e7	−	1.72279e7i	0.471094	−	0.153068i	0.534937	+	0.844892i	$0.320336\pi$
$104$	−1.04540e8	+	1.05323e8i	−0.893616	+	0.900302i
$105$	−2.85728e8	+	1.71012e8i	−2.35069	+	1.40692i
$106$	1.13518e8	−	1.40539e8i	0.899166	−	1.11320i
$107$			1.90829e8i			1.45583i	0.685668	+	0.727914i	$0.259510\pi$
$107$			1.90829e8i			1.45583i	−0.685668	+	0.727914i	$0.740490\pi$
$108$	−5.56539e7	−	9.58446e7i	−0.409073	−	0.704487i
$109$	2.02089e8	−	1.46826e8i	1.43165	−	1.04015i	0.441942	−	0.897043i	$-0.354290\pi$
$109$	2.02089e8	−	1.46826e8i	1.43165	−	1.04015i	0.989707	−	0.143110i	$-0.0457104\pi$
$110$	3.69850e7	+	2.10348e8i	0.252613	+	1.43671i
$111$	1.08400e8	−	1.49199e8i	0.714061	−	0.982821i
$112$	−2.01144e8	+	1.82929e8i	−1.27831	+	1.16255i
$113$	−4.91647e7	+	3.57203e7i	−0.301536	+	0.219079i	−0.728256	−	0.685305i	$-0.759669\pi$
$113$	−4.91647e7	+	3.57203e7i	−0.301536	+	0.219079i	0.426720	+	0.904384i	$0.359669\pi$
$114$	−2.18517e8	−	3.35573e8i	−1.29380	−	1.98686i
$115$	−3.63723e6	−	1.55133e6i	−0.0207960	−	0.00886979i
$116$	7.60403e7	+	7.80119e6i	0.419964	+	0.0430853i
$117$	−1.11195e8	+	3.42225e8i	−0.593395	+	1.82628i
$118$	−2.16935e6	+	5.67239e6i	−0.0111892	+	0.0292576i
$119$	−2.18476e8	−	7.09873e7i	−1.08947	−	0.353992i
$120$	−2.11832e8	−	2.51429e8i	−1.02157	−	1.21252i
$121$	−7.47152e7	−	2.29950e8i	−0.348552	−	1.07273i
$122$	4.00171e6	−	7.82163e7i	0.0180637	−	0.353068i
$123$	9.05089e7	−	1.24575e8i	0.395431	−	0.544264i
$124$	1.51935e8	−	1.69586e8i	0.642643	−	0.717303i
$125$	−1.52658e8	−	1.90526e8i	−0.625287	−	0.780395i
$126$	−2.35499e8	+	6.15780e8i	−0.934342	+	2.44311i
$127$	−1.63331e8	+	2.24806e8i	−0.627846	+	0.864157i	−0.997895	−	0.0648560i	$-0.979341\pi$
$127$	−1.63331e8	+	2.24806e8i	−0.627846	+	0.864157i	0.370048	+	0.929013i	$0.379341\pi$
$128$	−2.10075e8	−	1.67111e8i	−0.782589	−	0.622538i
$129$	2.27379e8	+	6.99802e8i	0.821093	+	2.52706i
$130$	−5.05957e7	+	3.58746e8i	−0.177149	+	1.25607i
$131$	−2.40551e8	−	7.81597e7i	−0.816811	−	0.265398i	−0.129331	−	0.991601i	$-0.541283\pi$
$131$	−2.40551e8	−	7.81597e7i	−0.816811	−	0.265398i	−0.687480	+	0.726204i	$0.741283\pi$
$132$	5.22979e8	+	4.68544e8i	1.72261	+	1.54332i
$133$	−2.49842e8	+	7.68933e8i	−0.798469	+	2.45744i
$134$	−6.05934e7	−	2.25019e8i	−0.187934	−	0.697911i
$135$	−2.48891e8	−	1.06155e8i	−0.749331	−	0.319600i
$136$	3.46449e7	−	2.24143e8i	0.101271	−	0.655193i
$137$	3.63098e8	−	2.63806e8i	1.03072	−	0.748863i	0.0622681	−	0.998059i	$-0.480167\pi$
$137$	3.63098e8	−	2.63806e8i	1.03072	−	0.748863i	0.968453	+	0.249197i	$0.0801666\pi$
$138$	−1.25532e7	+	3.38034e6i	−0.0346129	+	0.00932060i
$139$	2.90507e7	−	3.99848e7i	0.0778210	−	0.107111i	−0.768332	−	0.640052i	$-0.778913\pi$
$139$	2.90507e7	−	3.99848e7i	0.0778210	−	0.107111i	0.846153	+	0.532940i	$0.178913\pi$
$140$	−1.26162e8	+	6.51684e8i	−0.328410	+	1.69639i
$141$	−3.90830e7	+	2.83954e7i	−0.0988806	+	0.0718410i
$142$	−4.49922e8	−	3.63415e8i	−1.10658	−	0.893820i
$143$		−	7.73774e8i		−	1.85042i
$144$	−6.37350e8	−	1.32166e8i	−1.48227	−	0.307376i
$145$	1.60130e8	−	9.58399e7i	0.362244	−	0.216808i
$146$	3.60925e6	−	7.05453e7i	0.00794338	−	0.155259i
$147$	1.39807e9	−	4.54261e8i	2.99405	−	0.972827i
$148$	−7.73254e7	−	3.59394e8i	−0.161167	−	0.749073i
$149$	−7.33532e8			−1.48824			−0.744121	−	0.668044i	$-0.767132\pi$
$149$	−7.33532e8			−1.48824			−0.744121	+	0.668044i	$0.767132\pi$
$150$	−7.81686e8	−	1.82288e8i	−1.54407	−	0.360074i
$151$			4.58682e8i			0.882274i	0.897440	+	0.441137i	$0.145425\pi$
$151$			4.58682e8i			0.882274i	−0.897440	+	0.441137i	$0.854575\pi$
$152$	−7.88877e8	−	1.21934e8i	−1.47787	−	0.228428i
$153$	−1.69948e8	−	5.23045e8i	−0.310134	−	0.954494i
$154$	7.24365e7	−	1.41582e9i	0.128788	−	2.51725i
$155$	4.94049e7	−	5.53688e8i	0.0855939	−	0.959264i
$156$	5.98121e8	+	1.03006e9i	1.00993	+	1.73925i
$157$	4.79675e8			0.789493			0.394747	−	0.918790i	$-0.370832\pi$
$157$	4.79675e8			0.789493			0.394747	+	0.918790i	$0.370832\pi$
$158$	3.88704e8	+	3.13968e8i	0.623722	+	0.503798i
$159$	−8.52331e8	−	1.17313e9i	−1.33358	−	1.83552i
$160$	−6.55057e8	−	1.99340e7i	−0.999537	−	0.0304169i
$161$	2.12348e7	+	1.54280e7i	0.0316042	+	0.0229618i
$162$	1.47771e8	−	3.97920e7i	0.214551	−	0.0577745i
$163$	3.50563e8	+	4.82509e8i	0.496611	+	0.683526i	0.981590	−	0.191000i	$-0.0611729\pi$
$163$	3.50563e8	+	4.82509e8i	0.496611	+	0.683526i	−0.484979	+	0.874526i	$0.661173\pi$
$164$	−6.45634e7	−	3.00079e8i	−0.0892506	−	0.414820i
$165$	1.70749e9	+	1.52358e8i	2.30369	+	0.205555i
$166$	7.74250e7	+	2.87525e8i	0.101965	+	0.378654i
$167$	4.20681e8	+	1.36687e8i	0.540862	+	0.175737i	0.566692	−	0.823930i	$-0.308223\pi$
$167$	4.20681e8	+	1.36687e8i	0.540862	+	0.175737i	−0.0258301	+	0.999666i	$0.508223\pi$
$168$	9.97990e8	+	1.94075e9i	1.25282	+	2.43631i
$169$	1.53537e8	−	4.72538e8i	0.188220	−	0.579282i
$170$	−2.59720e8	−	4.89033e8i	−0.310964	−	0.585522i
$171$	−1.84087e9	+	5.98135e8i	−2.15297	+	0.699543i
$172$	1.34143e9	+	5.93252e8i	1.53269	+	0.677837i
$173$	3.54627e8	+	2.57652e8i	0.395902	+	0.287640i	0.767870	−	0.640606i	$-0.221317\pi$
$173$	3.54627e8	+	2.57652e8i	0.395902	+	0.287640i	−0.371968	+	0.928246i	$0.621317\pi$
$174$	2.19164e8	−	5.73069e8i	0.239096	−	0.625187i
$175$	7.05375e8	+	1.45900e9i	0.752087	+	1.55562i
$176$	1.39127e9	−	1.53222e8i	1.44998	−	0.159688i
$177$	3.94363e7	+	2.86522e7i	0.0401794	+	0.0291920i
$178$	4.05822e7	−	7.93207e8i	0.0404255	−	0.790145i
$179$	1.07550e7	−	3.49452e6i	0.0104761	−	0.00340389i	−0.303774	−	0.952744i	$-0.598247\pi$
$179$	1.07550e7	−	3.49452e6i	0.0104761	−	0.00340389i	0.314250	+	0.949340i	$0.398247\pi$
$180$	−1.43974e9	+	6.72689e8i	−1.37149	+	0.640803i
$181$	−5.93568e8	+	1.82681e9i	−0.553039	+	1.70208i	0.148026	+	0.988983i	$0.452708\pi$
$181$	−5.93568e8	+	1.82681e9i	−0.553039	+	1.70208i	−0.701065	+	0.713097i	$0.747292\pi$
$182$	8.59036e8	−	2.24620e9i	0.782935	−	2.04721i
$183$	−5.97864e8	−	1.94258e8i	−0.533087	−	0.173210i
$184$	−1.16788e7	+	2.31337e7i	−0.0101889	+	0.0201825i
$185$	−6.76339e8	−	5.89986e8i	−0.577401	−	0.503680i
$186$	−9.97279e8	−	1.53151e9i	−0.833230	−	1.27958i
$187$	6.95122e8	+	9.56753e8i	0.568453	+	0.782408i
$188$	−9.82793e6	+	9.57955e7i	−0.00786739	+	0.0766856i
$189$	1.45307e9	+	1.05572e9i	1.13878	+	0.827370i
$190$	−1.72117e9	+	9.14091e8i	−1.32071	+	0.701415i
$191$	2.80979e8	+	3.86735e8i	0.211126	+	0.290589i	0.901426	−	0.432934i	$-0.142522\pi$
$191$	2.80979e8	+	3.86735e8i	0.211126	+	0.290589i	−0.690300	+	0.723523i	$0.742522\pi$
$192$	−1.73364e9	+	1.27941e9i	−1.27571	+	0.941468i
$193$	1.51678e9			1.09318			0.546592	−	0.837399i	$-0.315925\pi$
$193$	1.51678e9			1.09318			0.546592	+	0.837399i	$0.315925\pi$
$194$	−6.31980e8	+	7.82416e8i	−0.446166	+	0.552371i
$195$	2.67487e9	+	1.14087e9i	1.84997	+	0.789036i
$196$	1.18520e9	−	2.67991e9i	0.803098	−	1.81592i
$197$	−4.87368e8	−	1.49997e9i	−0.323588	−	0.995901i	−0.972074	−	0.234675i	$-0.924597\pi$
$197$	−4.87368e8	−	1.49997e9i	−0.323588	−	0.995901i	0.648486	−	0.761227i	$-0.275403\pi$
$198$	2.84414e9	−	1.85204e9i	1.85051	−	1.20500i
$199$			7.86379e8i			0.501440i	0.968060	+	0.250720i	$0.0806674\pi$
$199$			7.86379e8i			0.501440i	−0.968060	+	0.250720i	$0.919333\pi$
$200$	−1.31039e9	+	9.18081e8i	−0.818995	+	0.573801i
$201$	−1.87047e9			−1.14595
$202$	−5.91716e8	−	9.08689e8i	−0.355392	−	0.545770i
$203$	−1.17812e9	+	3.82795e8i	−0.693755	+	0.225415i
$204$	−1.66491e9	−	7.36316e8i	−0.961327	−	0.425152i
$205$	−5.64714e8	−	4.92613e8i	−0.319752	−	0.278927i
$206$	−6.93920e8	−	5.60499e8i	−0.385337	−	0.311248i
$207$			6.28384e7i			0.0342250i
$208$	2.32488e9	+	4.82107e8i	1.24208	+	0.257567i
$209$	3.36732e9	−	2.44650e9i	1.76481	−	1.28221i
$210$	4.78757e9	+	2.33792e9i	2.46172	+	1.20214i
$211$	−3.14513e8	+	4.32890e8i	−0.158675	+	0.218398i	−0.880951	−	0.473208i	$-0.843096\pi$
$211$	−3.14513e8	+	4.32890e8i	−0.158675	+	0.218398i	0.722276	+	0.691605i	$0.243096\pi$
$212$	−2.87544e9	−	2.95000e8i	−1.42351	−	0.146042i
$213$	−3.75567e9	+	2.72865e9i	−1.82461	+	1.32565i
$214$	2.55862e9	−	1.66611e9i	1.21997	−	0.794417i
$215$	3.49055e9	−	7.99512e8i	1.63358	−	0.374172i
$216$	−7.99166e8	+	1.58301e9i	−0.367132	+	0.727225i
$217$	−1.14024e9	+	3.50929e9i	−0.514229	+	1.58264i
$218$	−3.73305e9	−	1.42766e9i	−1.65287	−	0.632121i
$219$	−5.39229e8	−	1.75206e8i	−0.234421	−	0.0761681i
$220$	2.49741e9	−	2.33242e9i	1.06610	−	0.995670i
$221$	6.19924e8	+	1.90793e9i	0.259878	+	0.799822i
$222$	−2.94687e9	−	1.50768e8i	−1.21325	−	0.0620723i
$223$	2.54746e9	−	3.50628e9i	1.03012	−	1.41784i	0.125266	−	0.992123i	$-0.460022\pi$
$223$	2.54746e9	−	3.50628e9i	1.03012	−	1.41784i	0.904856	−	0.425718i	$-0.139978\pi$
$224$	4.20886e9	+	1.09978e9i	1.67175	+	0.436833i
$225$	−1.83324e9	+	3.41928e9i	−0.715301	+	1.33415i
$226$	9.08185e8	+	3.47326e8i	0.348129	+	0.133138i
$227$	1.54714e9	−	2.12946e9i	0.582676	−	0.801984i	−0.411310	−	0.911496i	$-0.634929\pi$
$227$	1.54714e9	−	2.12946e9i	0.582676	−	0.801984i	0.993986	+	0.109511i	$0.0349286\pi$
$228$	−2.59148e9	+	5.85971e9i	−0.958979	+	2.16839i
$229$	−1.50791e9	−	4.64087e9i	−0.548319	−	1.68755i	−0.712965	−	0.701199i	$-0.752648\pi$
$229$	−1.50791e9	−	4.64087e9i	−0.548319	−	1.68755i	0.164646	−	0.986353i	$-0.447352\pi$
$230$	1.09562e7	+	6.23121e7i	0.00391515	+	0.0222670i
$231$	−1.08222e10	−	3.51633e9i	−3.80072	−	1.23493i
$232$	−5.59302e8	−	1.08765e9i	−0.193061	−	0.375438i
$233$	1.35460e9	−	4.16902e9i	0.459606	−	1.41452i	−0.406035	−	0.913857i	$-0.633089\pi$
$233$	1.35460e9	−	4.16902e9i	0.459606	−	1.41452i	0.865641	−	0.500665i	$-0.166911\pi$
$234$	5.55935e9	−	1.49703e9i	1.85422	−	0.499305i
$235$	1.20739e8	+	2.01732e8i	0.0395892	+	0.0661459i
$236$	9.49951e7	−	2.04387e7i	0.0306234	−	0.00658877i
$237$	3.24466e9	−	2.35738e9i	1.02843	−	0.747200i
$238$	9.55704e8	+	3.54909e9i	0.297862	+	1.10614i
$239$	−3.73865e9	+	5.14581e9i	−1.14584	+	1.57711i	−0.392115	+	0.919916i	$0.628256\pi$
$239$	−3.73865e9	+	5.14581e9i	−1.14584	+	1.57711i	−0.753722	+	0.657193i	$0.771744\pi$
$240$	−1.52164e9	+	5.03542e9i	−0.458636	+	1.51772i
$241$	3.15393e9	−	2.29147e9i	0.934942	−	0.679275i	−0.0122562	−	0.999925i	$-0.503901\pi$
$241$	3.15393e9	−	2.29147e9i	0.934942	−	0.679275i	0.947198	+	0.320650i	$0.103901\pi$
$242$	−2.43081e9	+	3.00944e9i	−0.708745	+	0.877454i
$243$		−	4.06883e9i		−	1.16693i
$244$	−1.08365e9	+	6.29244e8i	−0.305725	+	0.177525i
$245$	−1.59727e9	−	6.97345e9i	−0.443317	−	1.93546i
$246$	−2.46051e9	−	1.25885e8i	−0.671869	−	0.0343742i
$247$	6.71500e9	−	2.18184e9i	1.80409	−	0.586185i
$248$	−3.60031e9	−	5.56487e8i	−0.951773	−	0.147112i
$249$	2.39005e9			0.621742
$250$	−1.22172e9	+	3.71028e9i	−0.312759	+	0.949832i
$251$			2.01224e9i			0.506974i	0.967339	+	0.253487i	$0.0815775\pi$
$251$			2.01224e9i			0.506974i	−0.967339	+	0.253487i	$0.918422\pi$
$252$	1.03124e10	−	2.21877e9i	2.55716	−	0.550186i
$253$	−4.17558e7	−	1.28511e8i	−0.0101914	−	0.0313660i
$254$	4.44019e9	+	2.27170e8i	1.06676	+	0.0545778i
$255$	−4.33231e9	+	9.92316e8i	−1.02461	+	0.234687i
$256$	−4.06473e8	+	4.27569e9i	−0.0946393	+	0.995512i
$257$	3.92271e9			0.899194			0.449597	−	0.893231i	$-0.351568\pi$
$257$	3.92271e9			0.899194			0.449597	+	0.893231i	$0.351568\pi$
$258$	7.39765e9	−	9.15857e9i	1.66961	−	2.06704i
$259$	3.50173e9	+	4.81972e9i	0.778187	+	1.07108i
$260$	5.25177e9	−	2.45379e9i	1.14925	−	0.536963i
$261$	−2.39925e9	−	1.74316e9i	−0.517028	−	0.375643i
$262$	1.05227e9	+	3.90768e9i	0.223316	+	0.829304i
$263$	−1.70519e9	−	2.34700e9i	−0.356411	−	0.490557i	0.592734	−	0.805398i	$-0.298049\pi$
$263$	−1.70519e9	−	2.34700e9i	−0.356411	−	0.490557i	−0.949144	+	0.314841i	$0.898049\pi$
$264$	1.71613e9	−	1.11028e10i	0.353292	−	2.28570i
$265$	−6.05528e9	+	3.62416e9i	−1.22786	+	0.734893i
$266$	1.24911e10	−	3.36362e9i	2.49502	−	0.671863i
$267$	−6.06306e9	−	1.97001e9i	−1.19302	−	0.387635i
$268$	−2.48800e9	+	2.77705e9i	−0.482293	+	0.538324i
$269$	−4.63195e8	+	1.42557e9i	−0.0884616	+	0.272257i	−0.985495	−	0.169707i	$-0.945718\pi$
$269$	−4.63195e8	+	1.42557e9i	−0.0884616	+	0.272257i	0.897033	+	0.441963i	$0.145718\pi$
$270$	7.49718e8	+	4.26393e9i	0.141073	+	0.802334i
$271$	−2.11945e9	+	6.88651e8i	−0.392958	+	0.127680i	−0.498830	−	0.866700i	$-0.666237\pi$
$271$	−2.11945e9	+	6.88651e8i	−0.392958	+	0.127680i	0.105872	+	0.994380i	$0.466237\pi$
$272$	−3.30777e9	+	1.49245e9i	−0.604309	+	0.272662i
$273$	−1.56163e10	−	1.13459e10i	−2.81144	−	2.04263i
$274$	−6.70724e9	−	2.56511e9i	−1.18999	−	0.455097i
$275$	1.47707e9	−	8.21097e9i	0.258268	−	1.43570i
$276$	1.54924e8	+	1.38798e8i	0.0266982	+	0.0239193i
$277$	−5.69663e8	−	4.13884e8i	−0.0967606	−	0.0703007i	0.538353	−	0.842719i	$-0.319047\pi$
$277$	−5.69663e8	−	4.13884e8i	−0.0967606	−	0.0703007i	−0.635114	+	0.772419i	$0.719047\pi$
$278$	−7.89750e8	−	4.04053e7i	−0.132224	−	0.00676487i
$279$	−8.40145e9	+	2.72980e9i	−1.38656	+	0.450519i
$280$	9.83921e9	−	3.99821e9i	1.60077	−	0.650480i
$281$	8.63392e8	−	2.65725e9i	0.138479	−	0.426194i	−0.857636	−	0.514257i	$-0.828068\pi$
$281$	8.63392e8	−	2.65725e9i	0.138479	−	0.426194i	0.996115	+	0.0880633i	$0.0280678\pi$
$282$	7.21952e8	+	2.76103e8i	0.114159	+	0.0436591i
$283$	5.21996e9	+	1.69607e9i	0.813807	+	0.264422i	0.686209	−	0.727404i	$-0.259273\pi$
$283$	5.21996e9	+	1.69607e9i	0.813807	+	0.264422i	0.127598	+	0.991826i	$0.459273\pi$
$284$	−9.44413e8	+	9.20545e9i	−0.145174	+	1.41505i
$285$	3.49248e9	+	1.52477e10i	0.529365	+	2.31113i
$286$	−1.03747e10	+	6.75574e9i	−1.55064	+	1.00974i
$287$	2.92379e9	+	4.02426e9i	0.430942	+	0.593141i
$288$	3.79257e9	+	9.69945e9i	0.551268	+	1.40986i
$289$	3.16299e9	+	2.29805e9i	0.453427	+	0.329434i
$290$	−2.68309e9	−	1.31024e9i	−0.379353	−	0.185250i
$291$	4.74513e9	+	6.53111e9i	0.661723	+	0.910784i
$292$	−9.77376e8	+	5.67531e8i	−0.134441	+	0.0780653i
$293$	3.01642e9			0.409281			0.204641	−	0.978837i	$-0.434397\pi$
$293$	3.01642e9			0.409281			0.204641	+	0.978837i	$0.434397\pi$
$294$	−1.82971e10	−	1.47791e10i	−2.44902	−	1.97814i
$295$	1.55945e8	−	1.78770e8i	0.0205913	−	0.0236051i
$296$	−4.14360e9	+	4.17460e9i	−0.539773	+	0.543811i
$297$	−2.85729e9	−	8.79384e9i	−0.367222	−	1.13019i
$298$	6.40438e9	+	9.83511e9i	0.812105	+	1.24714i
$299$		−	2.29218e8i		−	0.0286790i
$300$	4.38072e9	+	1.20723e10i	0.540829	+	1.49041i
$301$	−2.37697e10			−2.89573
$302$	6.14996e9	−	4.00470e9i	0.739340	−	0.481440i
$303$	−8.27775e9	+	2.68960e9i	−0.982068	+	0.319093i
$304$	5.25272e9	+	1.16418e10i	0.615021	+	1.36309i
$305$	−1.20023e9	+	2.81405e9i	−0.138697	+	0.325187i
$306$	−5.52914e9	+	6.84529e9i	−0.630626	+	0.780739i
$307$			2.85062e8i			0.0320912i	0.999871	+	0.0160456i	$0.00510769\pi$
$307$			2.85062e8i			0.0320912i	−0.999871	+	0.0160456i	$0.994892\pi$
$308$	−1.96156e10	+	1.13902e10i	−2.17971	+	1.26569i
$309$	−5.79241e9	+	4.20843e9i	−0.635368	+	0.461622i
$310$	−7.85514e9	+	4.17177e9i	−0.850564	+	0.451725i
$311$	−4.31417e9	+	5.93795e9i	−0.461165	+	0.634739i	−0.974750	−	0.223300i	$-0.928317\pi$
$311$	−4.31417e9	+	5.93795e9i	−0.461165	+	0.634739i	0.513585	+	0.858039i	$0.328317\pi$
$312$	8.58876e9	−	1.70128e10i	0.906384	−	1.79539i
$313$	−4.45303e9	+	3.23532e9i	−0.463958	+	0.337085i	−0.795082	−	0.606502i	$-0.792572\pi$
$313$	−4.45303e9	+	3.23532e9i	−0.463958	+	0.337085i	0.331124	+	0.943587i	$0.392572\pi$
$314$	−4.18799e9	−	6.43143e9i	−0.430811	−	0.661590i
$315$	1.69290e10	−	1.94068e10i	1.71945	−	1.97112i
$316$	8.15913e8	−	7.95292e9i	0.0818268	−	0.797588i
$317$	1.29599e9	−	3.98864e9i	0.128341	−	0.394992i	−0.866154	−	0.499777i	$-0.833415\pi$
$317$	1.29599e9	−	3.98864e9i	0.128341	−	0.394992i	0.994495	+	0.104785i	$0.0334154\pi$
$318$	−8.28764e9	+	2.16705e10i	−0.810443	+	2.11914i
$319$	6.06505e9	+	1.97065e9i	0.585695	+	0.190304i
$320$	5.45195e9	+	8.95697e9i	0.519939	+	0.854203i
$321$	−7.57319e9	−	2.33079e10i	−0.713278	−	2.19524i
$322$	2.14581e7	−	4.19414e8i	0.00199603	−	0.0390139i
$323$	−6.34288e9	+	8.73023e9i	−0.582742	+	0.802076i
$324$	−1.82370e9	−	1.63388e9i	−0.165491	−	0.148266i
$325$	6.68717e9	−	1.24726e10i	0.599389	−	1.11796i
$326$	3.40870e9	−	8.91305e9i	0.301799	−	0.789143i
$327$	−1.88562e10	+	2.59534e10i	−1.64916	+	2.26988i
$328$	−3.45973e9	+	3.48561e9i	−0.298914	+	0.301151i
$329$	−4.82245e8	−	1.48420e9i	−0.0411608	−	0.126680i
$330$	−1.28651e10	−	2.42241e10i	−1.08482	−	2.04264i
$331$	−7.18884e9	−	2.33580e9i	−0.598890	−	0.194591i	−0.00614448	−	0.999981i	$-0.501956\pi$
$331$	−7.18884e9	−	2.33580e9i	−0.598890	−	0.194591i	−0.592745	+	0.805390i	$0.701956\pi$
$332$	3.17911e9	−	3.54845e9i	0.261670	−	0.292070i
$333$	−4.40738e9	+	1.35645e10i	−0.358430	+	1.10313i
$334$	−1.84022e9	−	6.83384e9i	−0.147872	−	0.549135i
$335$	−8.09027e8	+	9.06689e9i	−0.0642368	+	0.719912i
$336$	1.73080e10	−	3.03254e10i	1.35797	−	2.37930i
$337$	4.73365e8	−	3.43920e8i	0.0367009	−	0.0266648i	−0.569284	−	0.822141i	$-0.692779\pi$
$337$	4.73365e8	−	3.43920e8i	0.0367009	−	0.0266648i	0.605984	+	0.795476i	$0.292779\pi$
$338$	−7.67626e9	+	2.06707e9i	−0.588143	+	0.158376i
$339$	4.58739e9	−	6.31400e9i	0.347350	−	0.478086i
$340$	−4.28932e9	+	7.75199e9i	−0.320976	+	0.580093i
$341$	1.53679e10	−	1.11654e10i	1.13657	−	0.825769i
$342$	2.40922e10	+	1.94599e10i	1.76105	+	1.42245i
$343$			2.35712e10i			1.70297i
$344$	−3.75758e9	−	2.31653e10i	−0.268333	−	1.65426i
$345$	5.05817e8	+	4.51334e7i	0.0357040	+	0.00318582i
$346$	3.58357e8	−	7.00433e9i	0.0250041	−	0.488723i
$347$	1.69257e10	−	5.49951e9i	1.16743	−	0.379320i	0.339745	−	0.940518i	$-0.389659\pi$
$347$	1.69257e10	−	5.49951e9i	1.16743	−	0.379320i	0.827682	+	0.561197i	$0.189659\pi$
$348$	−9.59715e9	+	2.06487e9i	−0.654373	+	0.140792i
$349$	1.65162e10			1.11329			0.556646	−	0.830750i	$-0.312088\pi$
$349$	1.65162e10			1.11329			0.556646	+	0.830750i	$0.312088\pi$
$350$	1.34035e10	−	2.21959e10i	0.893198	−	1.47911i
$351$		−	1.56851e10i		−	1.03337i
$352$	−1.42014e10	−	1.73163e10i	−0.925042	−	1.12793i
$353$	9.21083e9	+	2.83480e10i	0.593198	+	1.82568i	0.563498	+	0.826117i	$0.309455\pi$
$353$	9.21083e9	+	2.83480e10i	0.593198	+	1.82568i	0.0297000	+	0.999559i	$0.490545\pi$
$354$	3.98510e7	−	7.78917e8i	0.00253762	−	0.0495996i
$355$	1.16024e10	+	1.93854e10i	0.730524	+	1.22056i
$356$	−1.09896e10	+	6.38128e9i	−0.684196	+	0.397290i
$357$	2.95019e10			1.81625
$358$	−1.40755e8	−	1.13692e8i	−0.00856903	−	0.00692145i
$359$	−5.28143e9	−	7.26927e9i	−0.317961	−	0.437636i	0.619882	−	0.784695i	$-0.287180\pi$
$359$	−5.28143e9	−	7.26927e9i	−0.317961	−	0.437636i	−0.937843	+	0.347059i	$0.887180\pi$
$360$	2.15895e10	+	1.34307e10i	1.28538	+	0.799626i
$361$	1.69863e10	+	1.23412e10i	1.00016	+	0.726658i
$362$	2.96761e10	−	7.99122e9i	1.72811	−	0.465349i
$363$	1.82514e10	+	2.51209e10i	1.05116	+	1.44680i
$364$	−3.76170e10	+	8.09348e9i	−2.14278	+	0.461031i
$365$	−1.08252e9	+	2.53807e9i	−0.0609909	+	0.142999i
$366$	2.61530e9	+	9.71214e9i	0.145746	+	0.541241i
$367$	−2.63199e10	−	8.55185e9i	−1.45084	−	0.471407i	−0.525582	−	0.850743i	$-0.676152\pi$
$367$	−2.63199e10	−	8.55185e9i	−1.45084	−	0.471407i	−0.925259	+	0.379336i	$0.876152\pi$
$368$	4.12141e8	−	4.53896e7i	0.0224727	−	0.00247494i
$369$	−3.67997e9	+	1.13258e10i	−0.198490	+	0.610890i
$370$	−2.00543e9	+	1.42194e10i	−0.107004	+	0.758707i
$371$	4.45504e10	−	1.44753e10i	2.35156	−	0.764068i
$372$	−1.18271e10	+	2.67428e10i	−0.617601	+	1.39648i
$373$	3.98906e8	+	2.89822e8i	0.0206080	+	0.0149726i	0.598042	−	0.801465i	$-0.295946\pi$
$373$	3.98906e8	+	2.89822e8i	0.0206080	+	0.0149726i	−0.577434	+	0.816438i	$0.695946\pi$
$374$	6.75901e9	−	1.76734e10i	0.345459	−	0.903304i
$375$	2.62068e10	+	1.72125e10i	1.32522	+	0.870401i
$376$	1.37022e9	−	7.04608e8i	0.0685551	−	0.0352530i
$377$	8.75184e9	+	6.35858e9i	0.433245	+	0.314771i
$378$	1.46835e9	−	2.86999e10i	0.0719221	−	1.40577i
$379$	1.03735e10	−	3.37057e9i	0.502771	−	0.163360i	−0.0466410	−	0.998912i	$-0.514852\pi$
$379$	1.03735e10	−	3.37057e9i	0.502771	−	0.163360i	0.549412	+	0.835551i	$0.314852\pi$
$380$	2.72833e10	+	1.50964e10i	1.30847	+	0.724000i
$381$	1.10277e10	−	3.39396e10i	0.523339	−	1.61067i
$382$	2.73210e9	−	7.14388e9i	0.128305	−	0.335491i
$383$	−3.79924e10	−	1.23445e10i	−1.76564	−	0.573690i	−0.767877	−	0.640597i	$-0.778687\pi$
$383$	−3.79924e10	−	1.23445e10i	−1.76564	−	0.573690i	−0.997759	+	0.0669070i	$0.978687\pi$
$384$	3.22904e10	+	1.20740e10i	1.48508	+	0.555299i
$385$	−2.17259e10	+	5.09382e10i	−0.988858	+	2.31847i
$386$	−1.32428e10	−	2.03368e10i	−0.596529	−	0.916081i
$387$	−3.34486e10	−	4.60380e10i	−1.49119	−	2.05245i
$388$	1.60083e10	+	1.64233e9i	0.706347	+	0.0724661i
$389$	−1.33675e10	−	9.71203e9i	−0.583782	−	0.424142i	0.256304	−	0.966596i	$-0.417495\pi$
$389$	−1.33675e10	−	9.71203e9i	−0.583782	−	0.424142i	−0.840086	+	0.542454i	$0.817495\pi$
$390$	−8.05732e9	−	4.58251e10i	−0.348283	−	1.98082i
$391$	2.05918e8	+	2.83422e8i	0.00881024	+	0.0121263i
$392$	−4.62799e10	+	7.50692e9i	−1.95996	+	0.317920i
$393$	3.24826e10			1.36170
$394$	−1.58562e10	+	1.96306e10i	−0.657983	+	0.814609i
$395$	−1.00237e10	−	1.67477e10i	−0.411757	−	0.687967i
$396$	−4.96638e10	−	2.19641e10i	−2.01957	−	0.893165i
$397$	−1.11799e9	−	3.44082e9i	−0.0450066	−	0.138516i	0.926028	−	0.377455i	$-0.123201\pi$
$397$	−1.11799e9	−	3.44082e9i	−0.0450066	−	0.138516i	−0.971035	+	0.238939i	$0.923201\pi$
$398$	1.05437e10	−	6.86578e9i	0.420204	−	0.273626i
$399$		−	1.03833e11i		−	4.09677i
$400$	2.37504e10	+	9.55393e9i	0.927751	+	0.373200i
$401$	−8.76490e9			−0.338976			−0.169488	−	0.985532i	$-0.554211\pi$
$401$	−8.76490e9			−0.338976			−0.169488	+	0.985532i	$0.554211\pi$
$402$	1.63309e10	+	2.50791e10i	0.625325	+	0.960302i
$403$	3.06462e10	−	9.95757e9i	1.16187	−	0.377514i
$404$	−7.01740e9	+	1.58673e10i	−0.263421	+	0.595632i
$405$	−5.95428e9	−	5.31293e8i	−0.221314	−	0.0197476i
$406$	1.54185e10	+	1.24540e10i	0.567465	+	0.458358i
$407$		−	3.06696e10i		−	1.11771i
$408$	4.66373e9	+	2.87517e10i	0.168303	+	1.03758i
$409$	2.79706e10	−	2.03218e10i	0.999558	−	0.726222i	0.0375649	−	0.999294i	$-0.488040\pi$
$409$	2.79706e10	−	2.03218e10i	0.999558	−	0.726222i	0.961993	+	0.273073i	$0.0880399\pi$
$410$	−1.67444e9	+	1.18726e10i	−0.0592564	+	0.420155i
$411$	−3.38794e10	+	4.66310e10i	−1.18732	+	1.63421i
$412$	−1.45658e9	+	1.41977e10i	−0.0505527	+	0.492751i
$413$	−1.27395e9	+	9.25578e8i	−0.0437877	+	0.0318136i
$414$	8.42530e8	−	5.48635e8i	0.0286803	−	0.0186759i
$415$	1.03376e9	−	1.15855e10i	0.0348519	−	0.390591i
$416$	−1.38343e10	−	3.53810e10i	−0.461937	−	1.18140i
$417$	−1.96142e9	+	6.03663e9i	−0.0648674	+	0.199641i
$418$	−6.22020e10	−	2.37885e10i	−2.03751	−	0.779224i
$419$	−2.08289e10	−	6.76772e9i	−0.675787	−	0.219577i	−0.0490373	−	0.998797i	$-0.515615\pi$
$419$	−2.08289e10	−	6.76772e9i	−0.675787	−	0.219577i	−0.626750	+	0.779220i	$0.715615\pi$
$420$	−1.04531e10	−	8.46034e10i	−0.335929	−	2.71888i
$421$	4.85357e9	+	1.49377e10i	0.154501	+	0.475506i	0.998110	−	0.0614521i	$-0.0195731\pi$
$421$	4.85357e9	+	1.49377e10i	0.154501	+	0.475506i	−0.843609	+	0.536959i	$0.819573\pi$
$422$	8.55012e9	+	4.37442e8i	0.269602	+	0.0137934i
$423$	2.19603e9	−	3.02258e9i	0.0685925	−	0.0944095i
$424$	2.11499e10	+	4.11293e10i	0.654401	+	1.27259i
$425$	2.93630e9	+	2.14295e10i	0.0900004	+	0.656836i
$426$	6.93758e10	+	2.65320e10i	2.10654	+	0.805624i
$427$	1.19363e10	−	1.64289e10i	0.359053	−	0.494194i
$428$	−4.46780e10	−	1.97591e10i	−1.33143	−	0.588832i
$429$	3.07077e10	+	9.45087e10i	0.906606	+	2.79025i
$430$	−4.11954e10	−	3.98205e10i	−1.20497	−	1.16475i
$431$	2.35048e10	+	7.63717e9i	0.681157	+	0.221321i	0.629102	−	0.777323i	$-0.283423\pi$
$431$	2.35048e10	+	7.63717e9i	0.681157	+	0.221321i	0.0520551	+	0.998644i	$0.483423\pi$
$432$	2.82023e10	−	3.10595e9i	0.809746	−	0.0891782i
$433$	2.00361e10	−	6.16649e10i	0.569984	−	1.75423i	−0.0826729	−	0.996577i	$-0.526346\pi$
$433$	2.00361e10	−	6.16649e10i	0.569984	−	1.75423i	0.652657	−	0.757654i	$-0.273654\pi$
$434$	5.70075e10	−	1.53511e10i	1.60684	−	0.432692i
$435$	−1.57548e10	+	1.80607e10i	−0.440003	+	0.504404i
$436$	1.34508e10	+	6.25171e10i	0.372223	+	1.73003i
$437$	9.97511e8	−	7.24734e8i	0.0273522	−	0.0198725i
$438$	2.35880e9	+	8.75963e9i	0.0640908	+	0.238007i
$439$	3.32161e9	−	4.57180e9i	0.0894314	−	0.123092i	−0.761957	−	0.647628i	$-0.775761\pi$
$439$	3.32161e9	−	4.57180e9i	0.0894314	−	0.123092i	0.851388	+	0.524536i	$0.175761\pi$
$440$	−5.30774e10	−	1.31210e10i	−1.41612	−	0.350070i
$441$	−9.19750e10	+	6.68238e10i	−2.43173	+	1.76676i
$442$	2.01688e10	−	2.49698e10i	0.528435	−	0.654223i
$443$			3.53044e10i			0.916671i	0.888779	+	0.458335i	$0.151554\pi$
$443$			3.53044e10i			0.916671i	−0.888779	+	0.458335i	$0.848446\pi$
$444$	2.37073e10	+	4.08277e10i	0.610029	+	1.05056i
$445$	−1.21718e10	+	2.85379e10i	−0.310395	+	0.727749i
$446$	−6.92535e10	−	3.54316e9i	−1.75026	−	0.0895469i
$447$	8.95934e10	−	2.91107e10i	2.24412	−	0.729159i
$448$	−2.20013e10	−	6.60340e10i	−0.546179	−	1.63929i
$449$	−1.93583e10			−0.476302			−0.238151	−	0.971228i	$-0.576541\pi$
$449$	−1.93583e10			−0.476302			−0.238151	+	0.971228i	$0.576541\pi$
$450$	6.18512e10	−	5.27351e9i	1.50834	−	0.128603i
$451$		−	2.56078e10i		−	0.618964i
$452$	−3.27236e9	−	1.52093e10i	−0.0783984	−	0.364381i
$453$	−1.82031e10	−	5.60233e10i	−0.432267	−	1.33038i
$454$	−4.20595e10	−	2.15185e9i	−0.990012	−	0.0506511i
$455$	−6.17525e10	+	7.07909e10i	−1.44082	+	1.65170i
$456$	1.01192e11	−	1.64141e10i	2.34039	−	0.379628i
$457$	−5.28365e10			−1.21135			−0.605675	−	0.795712i	$-0.707097\pi$
$457$	−5.28365e10			−1.21135			−0.605675	+	0.795712i	$0.707097\pi$
$458$	−4.90589e10	+	6.07368e10i	−1.11495	+	1.38035i
$459$	1.40907e10	+	1.93942e10i	0.317455	+	0.436939i
$460$	7.39817e8	−	6.90940e8i	0.0165232	−	0.0154315i
$461$	−3.73317e9	−	2.71231e9i	−0.0826559	−	0.0600531i	0.545690	−	0.837987i	$-0.316268\pi$
$461$	−3.73317e9	−	2.71231e9i	−0.0826559	−	0.0600531i	−0.628346	+	0.777934i	$0.716268\pi$
$462$	4.73405e10	+	1.75803e11i	1.03912	+	3.85886i
$463$	3.91774e10	+	5.39230e10i	0.852533	+	1.17341i	0.983299	+	0.181998i	$0.0582565\pi$
$463$	3.91774e10	+	5.39230e10i	0.852533	+	1.17341i	−0.130766	+	0.991413i	$0.541744\pi$
$464$	−9.69992e9	+	1.69952e10i	−0.209265	+	0.366653i
$465$	1.59392e10	+	6.95880e10i	0.340921	+	1.48841i
$466$	−6.77245e10	+	1.82369e10i	−1.43616	+	0.386730i
$467$	−2.52129e10	−	8.19218e9i	−0.530098	−	0.172239i	0.0317254	−	0.999497i	$-0.489900\pi$
$467$	−2.52129e10	−	8.19218e9i	−0.530098	−	0.172239i	−0.561823	+	0.827257i	$0.689900\pi$
$468$	−6.86100e10	−	6.14687e10i	−1.43022	−	1.28136i
$469$	1.86719e10	−	5.74663e10i	0.385920	−	1.18774i
$470$	1.65064e9	−	3.38015e9i	0.0338267	−	0.0692700i
$471$	−5.85874e10	+	1.90362e10i	−1.19048	+	0.386809i
$472$	−1.10343e9	−	1.09524e9i	−0.0222319	−	0.0220668i
$473$	9.89978e10	+	7.19261e10i	1.97779	+	1.43695i
$474$	−5.99363e10	−	2.29220e10i	−1.18734	−	0.454087i
$475$	7.54218e10	−	1.03344e10i	1.48157	−	0.203007i
$476$	3.92417e10	−	4.38007e10i	0.764399	−	0.853205i
$477$	9.07271e10	+	6.59171e10i	1.75252	+	1.27328i
$478$	1.01636e11	+	5.19992e9i	1.94687	+	0.0996059i
$479$	5.05513e10	−	1.64251e10i	0.960263	−	0.312008i	0.213384	−	0.976968i	$-0.431551\pi$
$479$	5.05513e10	−	1.64251e10i	0.960263	−	0.312008i	0.746879	+	0.664960i	$0.231551\pi$
$480$	8.07996e10	−	2.35616e10i	1.52210	−	0.443854i
$481$	1.60770e10	−	4.94798e10i	0.300347	−	0.924374i
$482$	−5.82604e10	−	2.22811e10i	−1.07941	−	0.412808i
$483$	−3.20589e9	−	1.04166e9i	−0.0589060	−	0.0191397i
$484$	6.15734e10	+	6.31699e9i	1.12205	+	0.115114i
$485$	3.37112e10	−	2.01766e10i	0.609266	−	0.364654i
$486$	−5.45545e10	+	3.55245e10i	−0.977879	+	0.636771i
$487$	−2.43244e10	−	3.34797e10i	−0.432441	−	0.595204i	0.536070	−	0.844173i	$-0.319908\pi$
$487$	−2.43244e10	−	3.34797e10i	−0.432441	−	0.595204i	−0.968511	+	0.248969i	$0.919908\pi$
$488$	1.78981e10	+	9.03567e9i	0.315593	+	0.159324i
$489$	−6.19664e10	−	4.50213e10i	−1.08373	−	0.787376i
$490$	−7.95537e10	+	8.23005e10i	−1.37999	+	1.42764i
$491$	4.64604e10	+	6.39472e10i	0.799386	+	1.10026i	0.992875	+	0.119158i	$0.0380195\pi$
$491$	4.64604e10	+	6.39472e10i	0.799386	+	1.10026i	−0.193489	+	0.981102i	$0.561980\pi$
$492$	1.97946e10	+	3.40893e10i	0.337820	+	0.581779i
$493$	−1.65337e10			−0.279886
$494$	−8.78818e10	−	7.09847e10i	−1.47568	−	1.19195i
$495$	−1.29231e11	+	2.96004e10i	−2.15252	+	0.493035i
$496$	2.39726e10	+	5.31312e10i	0.396085	+	0.877856i
$497$	−4.63412e10	−	1.42624e11i	−0.759525	−	2.33758i
$498$	−2.08673e10	−	3.20456e10i	−0.339273	−	0.521016i
$499$			1.20675e11i			1.94633i	0.230106	+	0.973166i	$0.426093\pi$
$499$			1.20675e11i			1.94633i	−0.230106	+	0.973166i	$0.573907\pi$
$500$	6.04137e10	−	1.60134e10i	0.966620	−	0.256215i
$501$	−5.68064e10			−0.901667
$502$	2.69800e10	−	1.75687e10i	0.424841	−	0.276646i
$503$	2.24524e10	−	7.29522e9i	0.350744	−	0.113964i	−0.128346	−	0.991729i	$-0.540967\pi$
$503$	2.24524e10	−	7.29522e9i	0.350744	−	0.113964i	0.479090	+	0.877766i	$0.340967\pi$
$504$	−1.19786e11	−	1.18896e11i	−1.85645	−	1.84266i
$505$	9.45719e9	+	4.12887e10i	0.145411	+	0.634842i
$506$	−1.35850e9	+	1.68187e9i	−0.0207232	+	0.0256561i
$507$			6.38090e10i			0.965717i
$508$	−3.57210e10	−	6.15170e10i	−0.536375	−	0.923721i
$509$	2.48333e10	−	1.80424e10i	0.369967	−	0.268797i	−0.387230	−	0.921983i	$-0.626568\pi$
$509$	2.48333e10	−	1.80424e10i	0.369967	−	0.268797i	0.757197	+	0.653186i	$0.226568\pi$
$510$	5.11298e10	+	4.94233e10i	0.755776	+	0.730552i
$511$	1.07657e10	−	1.48177e10i	0.157891	−	0.217318i
$512$	6.08769e10	−	3.18806e10i	0.885875	−	0.463924i
$513$	6.82583e10	−	4.95926e10i	0.985567	−	0.716056i
$514$	−3.42487e10	−	5.25953e10i	−0.490673	−	0.753519i
$515$	1.78945e10	+	2.98982e10i	0.254384	+	0.425027i
$516$	−1.87385e11	−	1.92244e10i	−2.64324	−	0.271177i
$517$	−2.48263e9	+	7.64074e9i	−0.0347496	+	0.106948i
$518$	3.40491e10	−	8.90313e10i	0.472918	−	1.23658i
$519$	−5.35392e10	−	1.73959e10i	−0.737908	−	0.239761i
$520$	−7.87528e10	−	4.89914e10i	−1.07709	−	0.670050i
$521$	−2.30312e10	−	7.08826e10i	−0.312583	−	0.962031i	−0.976738	−	0.214436i	$-0.931209\pi$
$521$	−2.30312e10	−	7.08826e10i	−0.312583	−	0.962031i	0.664155	−	0.747595i	$-0.268791\pi$
$522$	−2.42448e9	+	4.73883e10i	−0.0326541	+	0.638247i
$523$	9.85326e9	−	1.35618e10i	0.131696	−	0.181264i	−0.738076	−	0.674717i	$-0.764266\pi$
$523$	9.85326e9	−	1.35618e10i	0.131696	−	0.181264i	0.869772	+	0.493453i	$0.164266\pi$
$524$	4.32066e10	−	4.82262e10i	0.573092	−	0.639673i
$525$	−1.44056e11	−	1.50209e11i	−1.89624	−	1.97723i
$526$	−1.65804e10	+	4.33544e10i	−0.216597	+	0.566357i
$527$	−2.89479e10	+	3.98434e10i	−0.375297	+	0.516552i
$528$	−1.63849e11	+	7.39281e10i	−2.10818	+	0.951205i
$529$	2.41871e10	+	7.44401e10i	0.308859	+	0.950570i
$530$	1.01460e11	+	4.95463e10i	1.28586	+	0.627925i
$531$	−3.58538e9	−	1.16496e9i	−0.0450980	−	0.0146532i
$532$	−1.54158e11	−	1.38112e11i	−1.92450	−	1.72419i
$533$	1.34236e10	−	4.13135e10i	0.166326	−	0.511898i
$534$	2.65222e10	+	9.84928e10i	0.326171	+	1.21127i
$535$	−1.16258e11	+	2.66289e10i	−1.41908	+	0.325040i
$536$	5.89567e10	+	9.11272e9i	0.714290	+	0.110405i
$537$	−1.17493e9	+	8.53640e8i	−0.0141292	+	0.0102654i
$538$	2.31580e10	−	6.23600e9i	0.276421	−	0.0744350i
$539$	1.43695e11	−	1.97779e11i	1.70249	−	2.34328i
$540$	5.06247e10	−	4.72801e10i	0.595370	−	0.556036i
$541$	7.91166e9	−	5.74816e9i	0.0923588	−	0.0671026i	−0.540647	−	0.841249i	$-0.681821\pi$
$541$	7.91166e9	−	5.74816e9i	0.0923588	−	0.0671026i	0.633006	+	0.774147i	$0.281821\pi$
$542$	2.77381e10	+	2.24048e10i	0.321424	+	0.259624i
$543$		−	2.46683e11i		−	2.83753i
$544$	4.88904e10	+	3.13197e10i	0.558249	+	0.357621i
$545$	1.17650e11	+	1.02629e11i	1.33354	+	1.16328i
$546$	−1.57806e10	+	3.08442e11i	−0.177563	+	3.47059i
$547$	−1.11925e11	+	3.63668e10i	−1.25020	+	0.406214i	−0.857992	−	0.513663i	$-0.828288\pi$
$547$	−1.11925e11	+	3.63668e10i	−1.25020	+	0.406214i	−0.392207	+	0.919877i	$0.628288\pi$
$548$	2.41674e10	+	1.12326e11i	0.267984	+	1.24554i
$549$	4.86168e10			0.535176
$550$	−1.22988e11	+	5.18847e10i	−1.34404	+	0.567007i
$551$			5.81907e10i			0.631317i
$552$	5.08373e8	−	3.28903e9i	0.00547554	−	0.0354252i
$553$	4.00359e10	+	1.23218e11i	0.428103	+	1.31757i
$554$	−5.75653e8	+	1.12516e10i	−0.00611114	+	0.119446i
$555$	1.06022e11	+	4.52198e10i	1.11744	+	0.476603i
$556$	6.35347e9	+	1.09417e10i	0.0664832	+	0.114494i
$557$	−1.36282e11			−1.41585			−0.707927	−	0.706286i	$-0.750369\pi$
$557$	−1.36282e11			−1.41585			−0.707927	+	0.706286i	$0.750369\pi$
$558$	1.09953e11	+	8.88122e10i	1.13415	+	0.916085i
$559$	1.22011e11	+	1.67934e11i	1.24955	+	1.71986i
$560$	−1.39513e11	−	9.70151e10i	−1.41861	−	0.986478i
$561$	−1.22871e11	−	8.92713e10i	−1.24051	−	0.901281i
$562$	−4.31663e10	+	1.16239e10i	−0.432713	+	0.116521i
$563$	−9.88849e9	−	1.36103e10i	−0.0984229	−	0.135468i	0.756965	−	0.653455i	$-0.226681\pi$
$563$	−9.88849e9	−	1.36103e10i	−0.0984229	−	0.135468i	−0.855388	+	0.517988i	$0.826681\pi$
$564$	−2.60132e9	−	1.20905e10i	−0.0257086	−	0.119489i
$565$	−2.86222e10	−	2.49678e10i	−0.280872	−	0.245011i
$566$	−2.28342e10	−	8.47968e10i	−0.222495	−	0.826255i
$567$	3.77385e10	+	1.22620e10i	0.365134	+	0.118639i
$568$	1.31671e11	−	6.77092e10i	1.26502	−	0.650510i
$569$	−5.52578e10	+	1.70066e11i	−0.527163	+	1.62244i	0.232836	+	0.972516i	$0.425199\pi$
$569$	−5.52578e10	+	1.70066e11i	−0.527163	+	1.62244i	−0.759999	+	0.649924i	$0.774801\pi$
$570$	1.73947e11	−	1.79953e11i	1.64785	−	1.70474i
$571$	−1.88081e10	+	6.11111e9i	−0.176929	+	0.0574878i	−0.396142	−	0.918189i	$-0.629651\pi$
$571$	−1.88081e10	+	6.11111e9i	−0.176929	+	0.0574878i	0.219213	+	0.975677i	$0.429651\pi$
$572$	1.81160e11	+	8.01190e10i	1.69231	+	0.748431i
$573$	−4.96666e10	−	3.60849e10i	−0.460729	−	0.334739i
$574$	2.84295e10	−	7.43373e10i	0.261892	−	0.684792i
$575$	4.37557e8	−	2.43236e9i	0.00400280	−	0.0222514i
$576$	9.69368e10	−	1.35535e11i	0.880641	−	1.23129i
$577$	−1.68939e11	−	1.22741e11i	−1.52414	−	1.10735i	−0.959386	−	0.282096i	$-0.908970\pi$
$577$	−1.68939e11	−	1.22741e11i	−1.52414	−	1.10735i	−0.564756	−	0.825258i	$-0.691030\pi$
$578$	3.19626e9	−	6.24731e10i	0.0286372	−	0.559734i
$579$	−1.85259e11	+	6.01944e10i	−1.64841	+	0.535601i
$580$	5.85821e9	+	4.74141e10i	0.0517670	+	0.418982i
$581$	−2.38586e10	+	7.34293e10i	−0.209383	+	0.644414i
$582$	4.61393e10	−	1.20645e11i	0.402141	−	1.05152i
$583$	−2.29348e11	−	7.45197e10i	−1.98528	−	0.645055i
$584$	1.61428e10	+	8.14951e9i	0.138780	+	0.0700616i
$585$	−2.24008e11	−	1.99879e10i	−1.91267	−	0.170665i
$586$	−2.63361e10	−	4.04439e10i	−0.223337	−	0.342975i
$587$	−1.29798e11	−	1.78651e11i	−1.09324	−	1.50471i	−0.844057	−	0.536254i	$-0.819839\pi$
$587$	−1.29798e11	−	1.78651e11i	−1.09324	−	1.50471i	−0.249180	−	0.968457i	$-0.580161\pi$
$588$	−3.84066e10	+	3.74360e11i	−0.321290	+	3.13170i
$589$	1.40230e11	+	1.01883e11i	1.16514	+	0.846526i
$590$	−3.75847e9	−	5.30075e8i	−0.0310172	−	0.00437450i
$591$	1.19054e11	+	1.63864e11i	0.975876	+	1.34318i
$592$	9.21499e10	+	1.91090e10i	0.750254	+	0.155579i
$593$	6.64347e10			0.537250			0.268625	−	0.963245i	$-0.413431\pi$
$593$	6.64347e10			0.537250			0.268625	+	0.963245i	$0.413431\pi$
$594$	−9.29602e10	+	1.15088e11i	−0.746708	+	0.924454i
$595$	1.27603e10	−	1.43007e11i	0.101811	−	1.14101i
$596$	7.59522e10	−	1.71739e11i	0.601943	−	1.36108i
$597$	−3.12079e10	−	9.60482e10i	−0.245679	−	0.756122i
$598$	−3.07333e9	+	2.00127e9i	−0.0240328	+	0.0156495i
$599$			1.35172e10i			0.104997i	0.998621	+	0.0524987i	$0.0167186\pi$
$599$			1.35172e10i			0.104997i	−0.998621	+	0.0524987i	$0.983281\pi$
$600$	1.23616e11	−	1.64138e11i	0.953831	−	1.26650i
$601$	−8.21205e10			−0.629439			−0.314719	−	0.949185i	$-0.601910\pi$
$601$	−8.21205e10			−0.629439			−0.314719	+	0.949185i	$0.601910\pi$
$602$	2.07531e11	+	3.18702e11i	1.58014	+	2.42660i
$603$	1.37578e11	−	4.47016e10i	1.04059	−	0.338107i
$604$	−1.07389e11	−	4.74934e10i	−0.806887	−	0.356850i
$605$	1.29665e11	−	7.76061e10i	0.967833	−	0.579261i
$606$	1.08334e11	+	8.75045e10i	0.803294	+	0.648844i
$607$			1.12157e11i			0.826176i	0.910691	+	0.413088i	$0.135550\pi$
$607$			1.12157e11i			0.826176i	−0.910691	+	0.413088i	$0.864450\pi$
$608$	1.10231e11	−	1.72071e11i	0.806655	−	1.25919i
$609$	1.28704e11	−	9.35091e10i	0.935672	−	0.679806i
$610$	4.82096e10	−	8.47658e9i	0.348188	−	0.0612212i
$611$	−8.01053e9	+	1.10256e10i	−0.0574773	+	0.0791108i
$612$	1.40055e11	+	1.43686e10i	0.998374	+	0.102426i
$613$	3.53644e10	−	2.56938e10i	0.250452	−	0.181964i	−0.455475	−	0.890249i	$-0.650531\pi$
$613$	3.53644e10	−	2.56938e10i	0.250452	−	0.181964i	0.705927	+	0.708284i	$0.250531\pi$
$614$	3.82208e9	−	2.48884e9i	0.0268922	−	0.0175115i
$615$	8.85237e10	+	3.77566e10i	0.618813	+	0.263932i
$616$	3.23980e11	+	1.63558e11i	2.25007	+	1.13592i
$617$	3.28889e10	−	1.01222e11i	0.226939	−	0.698446i	−0.771150	−	0.636653i	$-0.780318\pi$
$617$	3.28889e10	−	1.01222e11i	0.226939	−	0.698446i	0.998089	−	0.0617927i	$-0.0196818\pi$
$618$	1.06999e11	+	4.09206e10i	0.733543	+	0.280536i
$619$	−9.25880e10	−	3.00837e10i	−0.630656	−	0.204912i	−0.0237901	−	0.999717i	$-0.507573\pi$
$619$	−9.25880e10	−	3.00837e10i	−0.630656	−	0.204912i	−0.606865	+	0.794805i	$0.707573\pi$
$620$	1.24517e11	+	6.88975e10i	0.842678	+	0.466269i
$621$	−8.46425e8	−	2.60503e9i	−0.00569144	−	0.0175164i
$622$	1.17282e11	+	6.00040e9i	0.783556	+	0.0400884i
$623$	1.21049e11	−	1.66609e11i	0.803540	−	1.10598i
$624$	−3.03094e11	+	3.33801e10i	−1.99912	+	0.220165i
$625$	9.47707e10	−	1.19589e11i	0.621089	−	0.783740i
$626$	8.22577e10	+	3.14586e10i	0.535647	+	0.204853i
$627$	−3.14193e11	+	4.32449e11i	−2.03295	+	2.79811i
$628$	−4.96671e10	+	1.12304e11i	−0.319323	+	0.722034i
$629$	2.45715e10	+	7.56233e10i	0.156975	+	0.483118i
$630$	−4.08010e11	−	5.75435e10i	−2.59005	−	0.365287i
$631$	1.38033e11	+	4.48497e10i	0.870695	+	0.282906i	0.710088	−	0.704113i	$-0.248655\pi$
$631$	1.38033e11	+	4.48497e10i	0.870695	+	0.282906i	0.160606	+	0.987019i	$0.448655\pi$
$632$	−1.13756e11	+	5.84964e10i	−0.713024	+	0.366658i
$633$	2.12351e10	−	6.53548e10i	0.132263	−	0.407064i
$634$	−6.47944e10	+	1.74479e10i	−0.401034	+	0.107991i
$635$	−1.59748e11	−	6.81350e10i	−0.982521	−	0.419059i
$636$	3.62914e11	−	7.80826e10i	2.21807	−	0.477228i
$637$	3.35501e11	−	2.43755e11i	2.03768	−	1.48046i
$638$	−2.65309e10	−	9.85251e10i	−0.160129	−	0.594653i
$639$	2.11027e11	−	2.90454e11i	1.26571	−	1.74210i
$640$	7.24937e10	−	1.51302e11i	0.432096	−	0.901827i
$641$	1.74078e11	−	1.26475e11i	1.03113	−	0.749157i	0.0625924	−	0.998039i	$-0.480063\pi$
$641$	1.74078e11	−	1.26475e11i	1.03113	−	0.749157i	0.968534	+	0.248882i	$0.0800632\pi$
$642$	−2.46389e11	+	3.05039e11i	−1.45038	+	1.79562i
$643$			1.49098e11i			0.872226i	0.899892	+	0.436113i	$0.143645\pi$
$643$			1.49098e11i			0.872226i	−0.899892	+	0.436113i	$0.856355\pi$
$644$	−5.81081e9	+	3.37415e9i	−0.0337826	+	0.0196165i
$645$	−3.94606e11	+	2.36177e11i	−2.27995	+	1.36458i
$646$	1.72433e11	+	8.82203e9i	0.990125	+	0.0506569i
$647$	2.51662e11	−	8.17699e10i	1.43615	−	0.466634i	0.515456	−	0.856916i	$-0.327622\pi$
$647$	2.51662e11	−	8.17699e10i	1.43615	−	0.466634i	0.920695	+	0.390282i	$0.127622\pi$
$648$	−5.98438e9	+	3.87172e10i	−0.0339406	+	0.219586i
$649$	8.10659e9			0.0456940
$650$	−2.25617e11	+	1.92364e10i	−1.26391	+	0.107763i
$651$		−	4.73876e11i		−	2.63840i
$652$	−1.49266e11	+	3.21153e10i	−0.825983	+	0.177714i
$653$	−6.29019e10	−	1.93592e11i	−0.345948	−	1.06472i	−0.961074	−	0.276290i	$-0.910895\pi$
$653$	−6.29019e10	−	1.93592e11i	−0.345948	−	1.06472i	0.615126	−	0.788429i	$-0.289105\pi$
$654$	5.12611e11	+	2.62263e10i	2.80206	+	0.143359i
$655$	1.40496e10	−	1.57456e11i	0.0763305	−	0.855447i
$656$	7.69412e10	+	1.59552e10i	0.415474	+	0.0861561i
$657$	4.38487e10			0.235340
$658$	−1.56895e10	+	1.94242e10i	−0.0836963	+	0.103619i
$659$	5.28296e10	+	7.27137e10i	0.280115	+	0.385545i	0.925772	−	0.378083i	$-0.123417\pi$
$659$	5.28296e10	+	7.27137e10i	0.280115	+	0.385545i	−0.645657	+	0.763627i	$0.723417\pi$
$660$	−2.12470e11	+	3.83993e11i	−1.11975	+	2.02370i
$661$	−1.49150e11	−	1.08364e11i	−0.781297	−	0.567646i	0.124071	−	0.992273i	$-0.460405\pi$
$661$	−1.49150e11	−	1.08364e11i	−0.781297	−	0.567646i	−0.905368	+	0.424628i	$0.860405\pi$
$662$	3.14469e10	+	1.16781e11i	0.163736	+	0.608050i
$663$	−1.51435e11	−	2.08432e11i	−0.783739	−	1.07872i
$664$	−7.53338e10	−	1.16441e10i	−0.387541	−	0.0599007i
$665$	−5.03316e11	−	4.49102e10i	−2.57368	−	0.229646i
$666$	2.20352e11	−	5.93367e10i	1.12001	−	0.301597i
$667$	1.79667e9	+	5.83773e8i	0.00907747	+	0.00294945i
$668$	−7.55606e10	+	8.43390e10i	−0.379481	+	0.423568i
$669$	−1.71998e11	+	5.29355e11i	−0.858654	+	2.64267i
$670$	1.28631e11	−	6.83147e10i	0.638334	−	0.339012i
$671$	−9.94264e10	+	3.23056e10i	−0.490469	+	0.159363i
$672$	−5.57715e11	+	3.27036e10i	−2.73486	+	0.160368i
$673$	1.37818e11	+	1.00131e11i	0.671808	+	0.488097i	0.870630	−	0.491939i	$-0.163712\pi$
$673$	1.37818e11	+	1.00131e11i	0.671808	+	0.488097i	−0.198822	+	0.980036i	$0.563712\pi$
$674$	−8.74414e9	−	3.34410e9i	−0.0423718	−	0.0162047i
$675$	2.99414e10	−	1.66443e11i	0.144231	−	0.801773i
$676$	9.47356e10	+	8.48750e10i	0.453656	+	0.406437i
$677$	7.93768e10	+	5.76706e10i	0.377867	+	0.274537i	0.760466	−	0.649378i	$-0.224971\pi$
$677$	7.93768e10	+	5.76706e10i	0.377867	+	0.274537i	−0.382599	+	0.923915i	$0.624971\pi$
$678$	−1.24709e11	−	6.38040e9i	−0.590175	−	0.0301946i
$679$	−2.48023e11	+	8.05874e10i	−1.16684	+	0.379130i
$680$	1.41388e11	−	1.01710e10i	0.661265	−	0.0475696i
$681$	−1.04459e11	+	3.21491e11i	−0.485687	+	1.49479i
$682$	−2.83881e11	−	1.08567e11i	−1.31219	−	0.501835i
$683$	−2.29589e11	−	7.45980e10i	−1.05504	−	0.342803i	−0.270395	−	0.962750i	$-0.587154\pi$
$683$	−2.29589e11	−	7.45980e10i	−1.05504	−	0.342803i	−0.784644	+	0.619947i	$0.787154\pi$
$684$	5.05708e10	−	4.92928e11i	0.231034	−	2.25195i
$685$	2.11384e11	+	1.84395e11i	0.960086	+	0.837505i
$686$	3.16041e11	−	2.05798e11i	1.42707	−	0.929275i
$687$	3.68352e11	+	5.06992e11i	1.65362	+	2.27601i
$688$	−2.77791e11	+	2.52635e11i	−1.23984	+	1.12756i
$689$	−3.30948e11	−	2.40448e11i	−1.46853	−	1.06695i
$690$	−3.81109e9	−	7.17599e9i	−0.0168133	−	0.0316581i
$691$	−1.11618e11	−	1.53629e11i	−0.489579	−	0.673847i	0.490732	−	0.871311i	$-0.336730\pi$
$691$	−1.11618e11	−	1.53629e11i	−0.489579	−	0.673847i	−0.980310	+	0.197464i	$0.936730\pi$
$692$	−9.70421e10	+	5.63492e10i	−0.423190	+	0.245733i
$693$	8.80030e11			3.81562
$694$	−2.21514e11	−	1.78923e11i	−0.954910	−	0.771309i
$695$	2.84135e10	+	1.21188e10i	0.121783	+	0.0519420i
$696$	1.11477e11	+	1.10649e11i	0.475061	+	0.471533i
$697$	2.05162e10	+	6.31422e10i	0.0869290	+	0.267540i
$698$	−1.44201e11	−	2.21448e11i	−0.607502	−	0.932932i
$699$			5.62961e11i			2.35814i
$700$	−4.14626e11	+	1.40770e10i	−1.72689	+	0.0586297i
$701$	4.05538e11			1.67942			0.839710	−	0.543036i	$-0.182725\pi$
$701$	4.05538e11			1.67942			0.839710	+	0.543036i	$0.182725\pi$
$702$	−2.10303e11	+	1.36944e11i	−0.865960	+	0.563892i
$703$	2.66158e11	−	8.64801e10i	1.08973	−	0.354075i
$704$	−1.08184e11	+	3.41598e11i	−0.440423	+	1.39067i
$705$	−2.27529e10	−	1.98479e10i	−0.0921044	−	0.0803447i
$706$	2.99668e11	−	3.71001e11i	1.20621	−	1.49333i
$707$		−	2.81165e11i		−	1.12534i
$708$	−1.07916e10	+	6.26632e9i	−0.0429489	+	0.0249390i
$709$	−3.36860e11	+	2.44743e11i	−1.33310	+	0.968557i	−0.333437	+	0.942772i	$0.608208\pi$
$709$	−3.36860e11	+	2.44743e11i	−1.33310	+	0.968557i	−0.999668	+	0.0257847i	$0.991792\pi$
$710$	1.58618e11	−	3.24815e11i	0.624192	−	1.27821i
$711$	−1.82314e11	+	2.50934e11i	−0.713414	+	0.981930i
$712$	1.81508e11	+	9.16325e10i	0.706279	+	0.356558i
$713$	4.55249e9	−	3.30758e9i	0.0176153	−	0.0127983i
$714$	−2.57577e11	−	3.95558e11i	−0.991094	−	1.52201i
$715$	4.71401e11	−	1.07975e11i	1.80371	−	0.413140i
$716$	−2.95453e8	+	2.87986e9i	−0.00112418	+	0.0109577i
$717$	2.52423e11	−	7.76879e11i	0.955108	−	2.93952i
$718$	−5.13540e10	+	1.34280e11i	−0.193231	+	0.505259i
$719$	1.26623e11	+	4.11423e10i	0.473802	+	0.153947i	0.536177	−	0.844105i	$-0.319868\pi$
$719$	1.26623e11	+	4.11423e10i	0.473802	+	0.153947i	−0.0623759	+	0.998053i	$0.519868\pi$
$720$	−8.41891e9	−	4.06731e11i	−0.0313275	−	1.51348i
$721$	−7.14725e10	−	2.19970e11i	−0.264483	−	0.813995i
$722$	1.71649e10	−	3.35500e11i	0.0631673	−	1.23465i
$723$	−2.94283e11	+	4.05045e11i	−1.07699	+	1.48235i
$724$	−3.66244e11	−	3.28124e11i	−1.33296	−	1.19422i
$725$	8.07329e10	+	8.41812e10i	0.292212	+	0.304693i
$726$	1.77467e11	−	4.64041e11i	0.638811	−	1.67036i
$727$	1.38175e11	−	1.90181e11i	0.494642	−	0.680816i	−0.486594	−	0.873628i	$-0.661761\pi$
$727$	1.38175e11	−	1.90181e11i	0.494642	−	0.680816i	0.981236	+	0.192812i	$0.0617607\pi$
$728$	4.36946e11	+	4.33701e11i	1.55562	+	1.54406i
$729$	1.42082e11	+	4.37284e11i	0.503071	+	1.54829i
$730$	4.34815e10	−	7.64525e9i	0.153113	−	0.0269216i
$731$	−3.01728e11	−	9.80375e10i	−1.05669	−	0.343339i
$732$	1.07385e11	−	1.19861e11i	0.374026	−	0.417479i
$733$	−3.02924e10	+	9.32304e10i	−0.104934	+	0.322955i	−0.989715	−	0.143053i	$-0.954308\pi$
$733$	−3.02924e10	+	9.32304e10i	−0.104934	+	0.322955i	0.884781	+	0.466008i	$0.154308\pi$
$734$	1.15134e11	+	4.27560e11i	0.396660	+	1.47303i
$735$	4.71837e11	+	7.88348e11i	1.61675	+	2.70127i
$736$	−4.20694e9	−	5.12966e9i	−0.0143369	−	0.0174814i
$737$	−2.51657e11	+	1.82839e11i	−0.852979	+	0.619725i
$738$	1.83985e11	−	4.95436e10i	0.620234	−	0.167017i
$739$	−7.42337e10	+	1.02174e11i	−0.248899	+	0.342580i	−0.915125	−	0.403170i	$-0.867908\pi$
$739$	−7.42337e10	+	1.02174e11i	−0.248899	+	0.342580i	0.666226	+	0.745750i	$0.267908\pi$
$740$	2.08161e11	−	9.72593e10i	0.694181	−	0.324343i
$741$	−7.33582e11	+	5.32979e11i	−2.43319	+	1.76782i
$742$	−5.83048e11	−	4.70945e11i	−1.92348	−	1.55365i
$743$			2.86631e11i			0.940521i	0.882528	+	0.470261i	$0.155840\pi$
$743$			2.86631e11i			0.940521i	−0.882528	+	0.470261i	$0.844160\pi$
$744$	4.61826e11	−	7.49115e10i	1.50725	−	0.244488i
$745$	−1.02359e11	−	4.46884e11i	−0.332278	−	1.45067i
$746$	4.03101e8	−	7.87890e9i	0.00130154	−	0.0254396i
$747$	−1.75794e11	+	5.71189e10i	−0.564575	+	0.183441i
$748$	−2.95975e11	+	6.36806e10i	−0.945473	+	0.203423i
$749$	7.91684e11			2.51550
$750$	1.97528e9	−	5.01658e11i	0.00624285	−	1.58549i
$751$		−	1.11018e11i		−	0.349007i	−0.984657	−	0.174504i	$-0.944168\pi$
$751$		−	1.11018e11i		−	0.349007i	0.984657	−	0.174504i	$-0.0558320\pi$
$752$	−2.14106e10	−	1.22199e10i	−0.0669510	−	0.0382118i
$753$	−7.98572e10	−	2.45775e11i	−0.248390	−	0.764466i
$754$	8.84387e9	−	1.72860e11i	0.0273626	−	0.534821i
$755$	−2.79440e11	+	6.40057e10i	−0.860003	+	0.196984i
$756$	−3.97625e11	+	2.30888e11i	−1.21727	+	0.706830i
$757$	6.13512e10			0.186827			0.0934135	−	0.995627i	$-0.470222\pi$
$757$	6.13512e10			0.186827			0.0934135	+	0.995627i	$0.470222\pi$
$758$	−1.35763e11	−	1.09659e11i	−0.411247	−	0.332176i
$759$	1.02001e10	+	1.40392e10i	0.0307353	+	0.0423035i
$760$	−3.57972e10	−	4.97617e11i	−0.107299	−	1.49156i
$761$	−7.59466e10	−	5.51784e10i	−0.226449	−	0.164524i	0.468776	−	0.883317i	$-0.344695\pi$
$761$	−7.59466e10	−	5.51784e10i	−0.226449	−	0.164524i	−0.695225	+	0.718793i	$0.744695\pi$
$762$	−5.51340e11	+	1.48465e11i	−1.63531	+	0.440358i
$763$	−6.09130e11	−	8.38396e11i	−1.79726	−	2.47372i
$764$	−1.19638e11	+	2.57407e10i	−0.351153	+	0.0755522i
$765$	2.94936e11	−	1.76523e11i	0.861157	−	0.515414i
$766$	1.66194e11	+	6.17176e11i	0.482725	+	1.79264i
$767$	1.30785e10	+	4.24946e9i	0.0377900	+	0.0122787i
$768$	−1.20037e11	−	5.38363e11i	−0.345041	−	1.54750i
$769$	2.72697e9	−	8.39276e9i	0.00779786	−	0.0239994i	−0.947082	−	0.320992i	$-0.895984\pi$
$769$	2.72697e9	−	8.39276e9i	0.00779786	−	0.0239994i	0.954880	+	0.296993i	$0.0959837\pi$
$770$	8.72660e11	−	1.53438e11i	2.48246	−	0.436485i
$771$	−4.79119e11	+	1.55675e11i	−1.35589	+	0.440557i
$772$	−1.57052e11	+	3.55117e11i	−0.442155	+	0.999775i
$773$	1.24234e11	+	9.02614e10i	0.347955	+	0.252804i	0.748011	−	0.663687i	$-0.231009\pi$
$773$	1.24234e11	+	9.02614e10i	0.347955	+	0.252804i	−0.400056	+	0.916491i	$0.631009\pi$
$774$	−3.25237e11	+	8.50427e11i	−0.906225	+	2.36959i
$775$	3.44214e11	−	4.71645e10i	0.954160	−	0.130740i
$776$	−1.17746e11	−	2.28976e11i	−0.324714	−	0.631457i
$777$	−6.18975e11	−	4.49711e11i	−1.69820	−	1.23381i
$778$	−1.35080e10	+	2.64024e11i	−0.0368701	+	0.720652i
$779$	2.22231e11	−	7.22071e10i	0.603468	−	0.196079i
$780$	−5.44071e11	+	5.08126e11i	−1.46986	+	1.37275i
$781$	−2.38568e11	+	7.34235e11i	−0.641220	+	1.97347i
$782$	2.00224e9	−	5.23546e9i	0.00535414	−	0.0140000i
$783$	1.22944e11	+	3.99468e10i	0.327084	+	0.106276i
$784$	5.04716e11	+	5.54973e11i	1.33593	+	1.46895i
$785$	6.69352e10	+	2.92229e11i	0.176269	+	0.769564i
$786$	−2.83602e11	−	4.35524e11i	−0.743053	−	1.14109i
$787$	8.62485e10	+	1.18711e11i	0.224829	+	0.309451i	0.906498	−	0.422210i	$-0.138746\pi$
$787$	8.62485e10	+	1.18711e11i	0.224829	+	0.309451i	−0.681669	+	0.731661i	$0.738746\pi$
$788$	4.01644e11	+	4.12058e10i	1.04169	+	0.106869i
$789$	3.01414e11	+	2.18990e11i	0.777778	+	0.565089i
$790$	−1.37036e11	+	2.80620e11i	−0.351824	+	0.720460i
$791$	1.48191e11	+	2.03967e11i	0.378543	+	0.521020i
$792$	1.39117e11	+	8.57653e11i	0.353574	+	2.17977i
$793$	−1.77341e11			−0.448452
$794$	−3.63731e10	+	4.50313e10i	−0.0915163	+	0.113301i
$795$	5.95763e11	−	6.82962e11i	1.49144	−	1.70973i
$796$	−1.84111e11	−	8.14241e10i	−0.458594	−	0.202815i
$797$	−2.07230e11	−	6.37788e11i	−0.513593	−	1.58068i	−0.785827	−	0.618447i	$-0.787762\pi$
$797$	−2.07230e11	−	6.37788e11i	−0.513593	−	1.58068i	0.272233	−	0.962231i	$-0.412238\pi$
$798$	−1.39218e12	+	9.06550e11i	−3.43307	+	2.23553i
$799$		−	2.08291e10i		−	0.0511074i
$800$	−7.92642e10	−	4.01857e11i	−0.193516	−	0.981097i
$801$	4.93032e11			1.19769
$802$	7.65253e10	+	1.17519e11i	0.184973	+	0.284060i
$803$	−8.96752e10	+	2.91372e10i	−0.215680	+	0.0700787i
$804$	1.93675e11	−	4.37926e11i	0.463499	−	1.04804i
$805$	−6.43592e9	+	1.50896e10i	−0.0153260	+	0.0359331i
$806$	−4.01079e11	−	3.23963e11i	−0.950363	−	0.767636i
$807$		−	1.92501e11i		−	0.453877i
$808$	2.74016e11	−	4.44473e10i	0.642880	−	0.104280i
$809$	−1.07869e11	+	7.83713e10i	−0.251827	+	0.182963i	−0.706536	−	0.707677i	$-0.749743\pi$
$809$	−1.07869e11	+	7.83713e10i	−0.251827	+	0.182963i	0.454709	+	0.890640i	$0.349743\pi$
$810$	4.48626e10	+	8.44730e10i	0.104218	+	0.196236i
$811$	1.48930e11	−	2.04985e11i	0.344270	−	0.473848i	−0.601412	−	0.798939i	$-0.705395\pi$
$811$	1.48930e11	−	2.04985e11i	0.344270	−	0.473848i	0.945683	+	0.325091i	$0.105395\pi$
$812$	3.23644e10	−	3.15464e11i	0.0744463	−	0.725649i
$813$	2.31540e11	−	1.68224e11i	0.529985	−	0.385057i
$814$	−4.11214e11	+	2.67773e11i	−0.936636	+	0.609914i
$815$	−2.45037e11	+	2.80902e11i	−0.555394	+	0.636685i
$816$	3.44781e11	−	3.13559e11i	0.777648	−	0.707226i
$817$	−3.45045e11	+	1.06194e12i	−0.774440	+	2.38348i
$818$	−5.16681e11	−	1.97599e11i	−1.15401	−	0.441338i
$819$	1.41977e12	+	4.61311e11i	3.15560	+	1.02532i
$820$	1.73806e11	−	8.12073e10i	0.384422	−	0.179614i
$821$	−1.76092e11	−	5.41956e11i	−0.387585	−	1.19286i	−0.934588	−	0.355733i	$-0.884231\pi$
$821$	−1.76092e11	−	5.41956e11i	−0.387585	−	1.19286i	0.547002	−	0.837131i	$-0.315769\pi$
$822$	9.21020e11	+	4.71213e10i	2.01735	+	0.103212i
$823$	4.34111e11	−	5.97503e11i	0.946241	−	1.30239i	−0.00693613	−	0.999976i	$-0.502208\pi$
$823$	4.34111e11	−	5.97503e11i	0.946241	−	1.30239i	0.953177	−	0.302413i	$-0.0977921\pi$
$824$	2.03078e11	−	1.04429e11i	0.440508	−	0.226522i
$825$	1.45449e11	+	1.06151e12i	0.313974	+	2.29143i
$826$	2.35328e10	+	8.99985e9i	0.0505536	+	0.0193337i
$827$	6.47689e10	−	8.91467e10i	0.138466	−	0.190583i	−0.734152	−	0.678985i	$-0.762420\pi$
$827$	6.47689e10	−	8.91467e10i	0.138466	−	0.190583i	0.872619	+	0.488402i	$0.162420\pi$
$828$	−1.47121e10	−	6.50649e9i	−0.0313006	−	0.0138428i
$829$	1.92135e10	+	5.91331e10i	0.0406807	+	0.125202i	0.969334	−	0.245746i	$-0.0790328\pi$
$829$	1.92135e10	+	5.91331e10i	0.0406807	+	0.125202i	−0.928654	+	0.370948i	$0.879033\pi$
$830$	−1.64363e11	+	8.72911e10i	−0.346331	+	0.183932i
$831$	8.60038e10	+	2.79443e10i	0.180349	+	0.0585989i
$832$	−3.53600e11	+	4.94396e11i	−0.737936	+	1.03177i
$833$	−1.95860e11	+	6.02795e11i	−0.406786	+	1.25196i
$834$	9.80635e10	−	2.64067e10i	0.202695	−	0.0545820i
$835$	−2.45702e10	+	2.75362e11i	−0.0505432	+	0.566446i
$836$	2.24125e11	+	1.04169e12i	0.458845	+	2.13263i
$837$	3.11520e11	−	2.26333e11i	0.634724	−	0.461154i
$838$	9.11139e10	+	3.38360e11i	0.184760	+	0.686124i
$839$	1.49468e11	−	2.05725e11i	0.301647	−	0.415182i	−0.631106	−	0.775696i	$-0.717399\pi$
$839$	1.49468e11	−	2.05725e11i	0.301647	−	0.415182i	0.932754	+	0.360514i	$0.117399\pi$
$840$	−1.04309e12	+	8.78817e11i	−2.09510	+	1.76515i
$841$	3.32578e11	−	2.41632e11i	0.664829	−	0.483027i
$842$	1.57908e11	−	1.95496e11i	0.314163	−	0.388946i
$843$			3.58820e11i			0.710504i
$844$	−6.87850e10	−	1.18458e11i	−0.135558	−	0.233451i
$845$	3.09306e11	+	2.75990e10i	0.606683	+	0.0541335i
$846$	−5.96997e10	−	3.05436e9i	−0.116544	−	0.00596265i
$847$	−9.53980e11	+	3.09967e11i	−1.85356	+	0.602257i
$848$	3.66800e11	−	6.42670e11i	0.709326	−	1.24281i
$849$	−7.04875e11			−1.35669
$850$	2.61688e11	−	2.26469e11i	0.501313	−	0.433843i
$851$		−	9.08535e9i		−	0.0173230i
$852$	−2.49974e11	−	1.16183e12i	−0.474391	−	2.20488i
$853$	1.35254e11	+	4.16270e11i	0.255479	+	0.786283i	0.993735	+	0.111763i	$0.0356497\pi$
$853$	1.35254e11	+	4.16270e11i	0.255479	+	0.786283i	−0.738256	+	0.674521i	$0.764350\pi$
$854$	−3.24492e11	−	1.66017e10i	−0.610060	−	0.0312120i
$855$	−6.21278e11	−	1.03804e12i	−1.16258	−	1.94244i
$856$	1.25151e11	+	7.71553e11i	0.233099	+	1.43705i
$857$	7.36465e11			1.36530			0.682651	−	0.730745i	$-0.260827\pi$
$857$	7.36465e11			1.36530			0.682651	+	0.730745i	$0.260827\pi$
$858$	9.99056e11	−	1.23687e12i	1.84349	−	2.28231i
$859$	−4.80040e11	−	6.60718e11i	−0.881667	−	1.21351i	−0.975956	−	0.217965i	$-0.930058\pi$
$859$	−4.80040e11	−	6.60718e11i	−0.881667	−	1.21351i	0.0942896	−	0.995545i	$-0.469942\pi$
$860$	−1.74237e11	+	9.00012e11i	−0.318527	+	1.64534i
$861$	−5.16817e11	−	3.75490e11i	−0.940425	−	0.683259i
$862$	−1.02819e11	−	3.81829e11i	−0.186228	−	0.691576i
$863$	−3.01665e11	−	4.15206e11i	−0.543853	−	0.748549i	0.445309	−	0.895377i	$-0.353094\pi$
$863$	−3.01665e11	−	4.15206e11i	−0.543853	−	0.748549i	−0.989162	+	0.146828i	$0.953094\pi$
$864$	−2.87875e11	−	3.51015e11i	−0.516594	−	0.629899i
$865$	−1.07482e11	+	2.52001e11i	−0.191986	+	0.450129i
$866$	−1.00173e12	+	2.69747e11i	−1.78106	+	0.479607i
$867$	−4.77527e11	−	1.55158e11i	−0.845126	−	0.274598i
$868$	−7.03552e11	−	6.30323e11i	−1.23942	−	1.11041i
$869$	2.06107e11	−	6.34333e11i	0.361421	−	1.11234i
$870$	3.79710e11	+	5.35523e10i	0.662788	+	0.0934762i
$871$	−5.01846e11	+	1.63060e11i	−0.871963	+	0.283318i
$872$	7.20784e11	−	7.26177e11i	1.24663	−	1.25596i
$873$	−5.05100e11	−	3.66976e11i	−0.869601	−	0.631802i
$874$	−1.84263e10	−	7.04695e9i	−0.0315786	−	0.0120769i
$875$	−7.90426e11	+	6.33323e11i	−1.34843	+	1.08042i
$876$	9.68538e10	−	1.08106e11i	0.164475	−	0.183583i
$877$	−2.73265e10	−	1.98539e10i	−0.0461941	−	0.0335620i	0.564449	−	0.825468i	$-0.309089\pi$
$877$	−2.73265e10	−	1.98539e10i	−0.0461941	−	0.0335620i	−0.610643	+	0.791906i	$0.709089\pi$
$878$	−9.02988e10	−	4.61988e9i	−0.151951	−	0.00777414i
$879$	−3.68426e11	+	1.19709e11i	−0.617155	+	0.200526i
$880$	2.87489e11	+	8.26214e11i	0.479391	+	1.37772i
$881$	6.28913e10	−	1.93559e11i	0.104397	−	0.321300i	−0.885192	−	0.465227i	$-0.845973\pi$
$881$	6.28913e10	−	1.93559e11i	0.104397	−	0.321300i	0.989588	+	0.143926i	$0.0459729\pi$
$882$	1.69899e12	+	6.49761e11i	2.80748	+	1.07369i
$883$	2.08421e10	+	6.77202e9i	0.0342846	+	0.0111398i	0.326109	−	0.945332i	$-0.394262\pi$
$883$	2.08421e10	+	6.77202e9i	0.0342846	+	0.0111398i	−0.291824	+	0.956472i	$0.594262\pi$
$884$	−5.10884e11	−	5.24130e10i	−0.836591	−	0.0858282i
$885$	−1.19525e10	+	2.80237e10i	−0.0194844	+	0.0456828i
$886$	4.73357e11	−	3.08238e11i	0.768164	−	0.500209i
$887$	−5.56597e11	−	7.66090e11i	−0.899180	−	1.23761i	−0.970729	−	0.240177i	$-0.922794\pi$
$887$	−5.56597e11	−	7.66090e11i	−0.899180	−	1.23761i	0.0715494	−	0.997437i	$-0.477206\pi$
$888$	3.40427e11	−	6.74327e11i	0.547485	−	1.08447i
$889$	9.32639e11	+	6.77602e11i	1.49316	+	1.08485i
$890$	4.88903e11	−	8.59627e10i	0.779225	−	0.137009i
$891$	−1.20072e11	−	1.65264e11i	−0.190515	−	0.262222i
$892$	5.57138e11	+	9.59478e11i	0.880042	+	1.51557i
$893$	−7.33086e10			−0.115279
$894$	−1.17254e12	−	9.47097e11i	−1.83560	−	1.48267i
$895$	3.62973e9	+	6.06457e9i	0.00565694	+	0.00945166i
$896$	−6.93286e11	+	8.71526e11i	−1.07567	+	1.35222i
$897$	9.09665e9	+	2.79966e10i	0.0140511	+	0.0432450i
$898$	1.69015e11	+	2.59554e11i	0.259909	+	0.399138i
$899$			2.65573e11i			0.406580i
$900$	−6.10722e11	−	7.83252e11i	−0.930837	−	1.19380i
$901$	6.25217e11			0.948705
$902$	−3.43346e11	+	2.23579e11i	−0.518688	+	0.337757i
$903$	2.90323e12	−	9.43317e11i	4.36647	−	1.41875i
$904$	−1.75354e11	+	1.76666e11i	−0.262568	+	0.264533i
$905$	−1.19577e12	−	1.06697e11i	−1.78259	−	0.159058i
$906$	−5.92226e11	+	7.33198e11i	−0.878971	+	1.08820i
$907$			6.75287e11i			0.997837i	0.866649	+	0.498918i	$0.166269\pi$
$907$			6.75287e11i			0.997837i	−0.866649	+	0.498918i	$0.833731\pi$
$908$	3.38365e11	+	5.82717e11i	0.497785	+	0.857263i
$909$	5.44569e11	−	3.95653e11i	0.797623	−	0.579507i
$910$	1.48831e12	+	2.09903e11i	2.17034	+	0.306093i
$911$	8.62508e10	−	1.18714e11i	0.125225	−	0.172357i	−0.741802	−	0.670619i	$-0.766028\pi$
$911$	8.62508e10	−	1.18714e11i	0.125225	−	0.172357i	0.867026	+	0.498263i	$0.166028\pi$
$912$	−1.10358e12	−	1.21347e12i	−1.59523	−	1.75407i
$913$	3.21562e11	−	2.33628e11i	0.462787	−	0.336235i
$914$	4.61310e11	+	7.08426e11i	0.661010	+	1.01510i
$915$	3.49188e10	−	3.91340e11i	0.0498167	−	0.558303i
$916$	1.24268e12	+	1.27490e11i	1.76513	+	0.181090i
$917$	−3.24257e11	+	9.97960e11i	−0.458577	+	1.41135i
$918$	1.37011e11	−	3.58255e11i	0.192923	−	0.504454i
$919$	−7.06369e10	−	2.29513e10i	−0.0990306	−	0.0321770i	0.259083	−	0.965855i	$-0.416580\pi$
$919$	−7.06369e10	−	2.29513e10i	−0.0990306	−	0.0321770i	−0.358113	+	0.933678i	$0.616580\pi$
$920$	−1.57233e10	−	3.88687e9i	−0.0219479	−	0.00542561i
$921$	−1.13129e10	−	3.48174e10i	−0.0157229	−	0.0483902i
$922$	−3.77243e9	+	7.37348e10i	−0.00522032	+	0.102035i
$923$	−7.69771e11	+	1.05950e12i	−1.06061	+	1.45980i
$924$	1.94383e12	−	2.16965e12i	2.66667	−	2.97648i
$925$	2.65055e11	−	4.94370e11i	0.362050	−	0.675282i
$926$	3.80941e11	−	9.96082e11i	0.518100	−	1.35472i
$927$	3.25469e11	−	4.47970e11i	0.440748	−	0.606638i
$928$	3.12559e11	−	1.83280e10i	0.421444	−	0.0247129i
$929$	2.06450e11	+	6.35388e11i	0.277174	+	0.853053i	0.988636	+	0.150329i	$0.0480332\pi$
$929$	2.06450e11	+	6.35388e11i	0.277174	+	0.853053i	−0.711462	+	0.702724i	$0.751967\pi$
$930$	7.93866e11	−	8.21276e11i	1.06124	−	1.09789i
$931$	2.12155e12	+	6.89334e11i	2.82394	+	0.917553i
$932$	8.35814e11	+	7.48819e11i	1.10776	+	0.992460i
$933$	2.91281e11	−	8.96471e11i	0.384402	−	1.18307i
$934$	1.10291e11	+	4.09577e11i	0.144929	+	0.538206i
$935$	−4.85877e11	+	5.56992e11i	−0.635740	+	0.728790i
$936$	−2.25140e11	+	1.45659e12i	−0.293325	+	1.89773i
$937$	8.10461e11	−	5.88834e11i	1.05141	−	0.763897i	0.0789328	−	0.996880i	$-0.474849\pi$
$937$	8.10461e11	−	5.88834e11i	1.05141	−	0.763897i	0.972481	+	0.232983i	$0.0748487\pi$
$938$	−9.33524e11	+	2.51381e11i	−1.20591	+	0.324728i
$939$	4.15497e11	−	5.71882e11i	0.534448	−	0.735604i
$940$	−5.97323e10	+	7.38017e9i	−0.0765064	+	0.00945267i
$941$	6.19968e9	−	4.50433e9i	0.00790698	−	0.00574476i	−0.583825	−	0.811880i	$-0.698444\pi$
$941$	6.19968e9	−	4.50433e9i	0.00790698	−	0.00574476i	0.591732	+	0.806135i	$0.298444\pi$
$942$	7.66756e11	+	6.19331e11i	0.973764	+	0.786537i
$943$		−	7.58588e9i		−	0.00959310i
$944$	−5.05088e9	+	2.43571e10i	−0.00636033	+	0.0306717i
$945$	−4.40401e11	+	1.03256e12i	−0.552232	+	1.29476i
$946$	1.00039e11	−	1.95533e12i	0.124912	−	2.44150i
$947$	4.96860e11	−	1.61439e11i	0.617780	−	0.200729i	0.0166255	−	0.999862i	$-0.494708\pi$
$947$	4.96860e11	−	1.61439e11i	0.617780	−	0.200729i	0.601154	+	0.799133i	$0.294708\pi$
$948$	2.15961e11	+	1.00375e12i	0.267389	+	1.24277i
$949$	−1.59948e11			−0.197204
$950$	−7.97062e11	−	9.21019e11i	−0.978583	−	1.13077i
$951$			5.38604e11i			0.658488i
$952$	−9.29890e11	−	1.43730e11i	−1.13210	−	0.174984i
$953$	−1.60359e11	−	4.93533e11i	−0.194411	−	0.598335i	−0.999983	−	0.00583730i	$-0.998142\pi$
$953$	−1.60359e11	−	4.93533e11i	−0.194411	−	0.598335i	0.805572	−	0.592498i	$-0.201858\pi$
$954$	9.16812e10	−	1.79197e12i	0.110685	−	2.16341i
$955$	−1.96399e11	+	2.25145e11i	−0.236116	+	0.270676i
$956$	−8.17654e11	−	1.40813e12i	−0.978899	−	1.68582i
$957$	−8.18991e11			−0.976408
$958$	−6.61584e11	−	5.34380e11i	−0.785458	−	0.634437i
$959$	−1.09444e12	−	1.50636e12i	−1.29395	−	1.78097i
$960$	−1.02136e12	−	8.77639e11i	−1.20253	−	1.03331i
$961$	−5.00157e10	−	3.63385e10i	−0.0586426	−	0.0426063i
$962$	−8.03786e11	+	2.16444e11i	−0.938513	+	0.252724i
$963$	1.11405e12	+	1.53336e12i	1.29539	+	1.78295i
$964$	2.09923e11	+	9.75683e11i	0.243081	+	1.12980i
$965$	2.11656e11	+	9.24057e11i	0.244073	+	1.06559i
$966$	1.40238e10	+	5.20787e10i	0.0161049	+	0.0598070i
$967$	1.86603e11	+	6.06310e10i	0.213409	+	0.0693408i	0.413770	−	0.910381i	$-0.364212\pi$
$967$	1.86603e11	+	6.06310e10i	0.213409	+	0.0693408i	−0.200361	+	0.979722i	$0.564212\pi$
$968$	−4.52893e11	−	8.80722e11i	−0.515815	−	1.00308i
$969$	4.28254e11	−	1.31803e12i	0.485743	−	1.49496i
$970$	−5.64854e11	−	2.75836e11i	−0.638042	−	0.311576i
$971$	5.80606e11	−	1.88650e11i	0.653138	−	0.212217i	0.0363405	−	0.999339i	$-0.488430\pi$
$971$	5.80606e11	−	1.88650e11i	0.653138	−	0.212217i	0.616797	+	0.787122i	$0.288430\pi$
$972$	9.52618e11	+	4.21300e11i	1.06722	+	0.471983i
$973$	−1.65883e11	−	1.20521e11i	−0.185076	−	0.134466i
$974$	−2.36518e11	+	6.18447e11i	−0.262802	+	0.687174i
$975$	−3.21785e11	+	1.78879e12i	−0.356080	+	1.97943i
$976$	−3.51170e10	−	3.18865e11i	−0.0387006	−	0.351405i
$977$	−2.22638e11	−	1.61756e11i	−0.244354	−	0.177534i	0.458867	−	0.888505i	$-0.348256\pi$
$977$	−2.22638e11	−	1.61756e11i	−0.244354	−	0.177534i	−0.703221	+	0.710971i	$0.748256\pi$
$978$	−6.26181e10	+	1.22392e12i	−0.0684454	+	1.33781i
$979$	−1.00830e12	+	3.27617e11i	−1.09764	+	0.356645i
$980$	1.79805e12	+	3.48091e11i	1.94939	+	0.377389i
$981$	7.66669e11	−	2.35957e12i	0.827813	−	2.54775i
$982$	4.51757e11	−	1.18125e12i	0.485801	−	1.27027i
$983$	−1.34596e12	−	4.37330e11i	−1.44152	−	0.468377i	−0.519147	−	0.854685i	$-0.673750\pi$
$983$	−1.34596e12	−	4.37330e11i	−1.44152	−	0.468377i	−0.922370	+	0.386308i	$0.873750\pi$
$984$	2.84242e11	−	5.63034e11i	0.303185	−	0.600557i
$985$	8.45805e11	−	5.06225e11i	0.898515	−	0.537773i
$986$	1.44354e11	+	2.21682e11i	0.152729	+	0.234543i
$987$	1.17803e11	+	1.62141e11i	0.124133	+	0.170854i
$988$	−1.84469e11	+	1.79807e12i	−0.193596	+	1.88703i
$989$	2.93265e10	+	2.13069e10i	0.0306531	+	0.0222708i
$990$	1.52518e12	+	1.47428e12i	1.58775	+	1.53476i
$991$	8.34695e11	+	1.14886e12i	0.865432	+	1.19117i	0.980247	+	0.197778i	$0.0633726\pi$
$991$	8.34695e11	+	1.14886e12i	0.865432	+	1.19117i	−0.114815	+	0.993387i	$0.536627\pi$
$992$	5.03075e11	−	7.85305e11i	0.519501	−	0.810945i
$993$	9.70741e11			0.998404
$994$	−1.50768e12	+	1.86657e12i	−1.54442	+	1.91205i
$995$	−4.79080e11	+	1.09733e11i	−0.488783	+	0.111956i
$996$	−2.47474e11	+	5.59573e11i	−0.251473	+	0.568616i
$997$	2.87595e11	+	8.85126e11i	0.291072	+	0.895828i	0.984513	+	0.175314i	$0.0560941\pi$
$997$	2.87595e11	+	8.85126e11i	0.291072	+	0.895828i	−0.693440	+	0.720514i	$0.743906\pi$
$998$	1.61800e12	−	1.05360e12i	1.63101	−	1.06207i
$999$		−	6.21698e11i		−	0.624191i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.j.b.91.37	yes	464
4.3	odd	2	inner	100.9.j.b.91.9	yes	464
25.11	even	5	inner	100.9.j.b.11.9	✓	464
100.11	odd	10	inner	100.9.j.b.11.37	yes	464

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.9.j.b.11.9	✓	464	25.11	even	5	inner
100.9.j.b.11.37	yes	464	100.11	odd	10	inner
100.9.j.b.91.9	yes	464	4.3	odd	2	inner
100.9.j.b.91.37	yes	464	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.73089 - 13.4079i) q^{2} +(-122.140 + 39.6856i) q^{3} +(-103.543 + 234.126i) q^{4} +(139.543 + 609.223i) q^{5} +(1598.49 + 1291.15i) q^{6} -4148.65i q^{7} +(4043.16 - 655.829i) q^{8} +(8035.23 - 5837.94i) q^{9} +(6950.07 - 7190.03i) q^{10} +(-12553.6 + 17278.6i) q^{11} +(3355.32 - 32705.2i) q^{12} +(-29310.4 + 21295.2i) q^{13} +(-55624.6 + 36221.4i) q^{14} +(-41221.1 - 68872.6i) q^{15} +(-44093.6 - 48484.2i) q^{16} +(17111.0 - 52662.1i) q^{17} +(-148429. - 56765.2i) q^{18} +(-185346. - 60222.4i) q^{19} +(-157083. - 30410.4i) q^{20} +(164642. + 506715. i) q^{21} +(341273. + 17460.3i) q^{22} +(-3718.80 + 5118.49i) q^{23} +(-467803. + 240558. i) q^{24} +(-351681. + 170025. i) q^{25} +(541430. + 207064. i) q^{26} +(-254472. + 350251. i) q^{27} +(971305. + 429564. i) q^{28} +(-92269.9 - 283978. i) q^{29} +(-563539. + 1.15401e6i) q^{30} +(-845889. - 274846. i) q^{31} +(-265095. + 1.01451e6i) q^{32} +(847586. - 2.60860e6i) q^{33} +(-855482. + 230365. i) q^{34} +(2.52745e6 - 578914. i) q^{35} +(534817. + 2.48573e6i) q^{36} +(-1.16176e6 + 844066. i) q^{37} +(810776. + 3.01089e6i) q^{38} +(2.73485e6 - 3.76420e6i) q^{39} +(963739. + 2.37167e6i) q^{40} +(-970017. + 704759. i) q^{41} +(5.35651e6 - 6.63157e6i) q^{42} -5.72951e6i q^{43} +(-2.74552e6 - 4.72820e6i) q^{44} +(4.67787e6 + 4.08061e6i) q^{45} +(101097. + 5172.32i) q^{46} +(357755. - 116241. i) q^{47} +(7.30972e6 + 4.17197e6i) q^{48} -1.14465e7 q^{49} +(5.35017e6 + 3.23082e6i) q^{50} +7.11120e6i q^{51} +(-1.95087e6 - 9.06729e6i) q^{52} +(3.48916e6 + 1.07385e7i) q^{53} +(6.91790e6 + 353934. i) q^{54} +(-1.22783e7 - 5.23686e6i) q^{55} +(-2.72080e6 - 1.67736e7i) q^{56} +2.50281e7 q^{57} +(-3.00194e6 + 3.71652e6i) q^{58} +(-223104. - 307076. i) q^{59} +(2.03930e7 - 2.51964e6i) q^{60} +(3.96007e6 + 2.87716e6i) q^{61} +(3.70026e6 + 1.37412e7i) q^{62} +(-2.42195e7 - 3.33353e7i) q^{63} +(1.59170e7 - 5.30324e6i) q^{64} +(-1.70636e7 - 1.48850e7i) q^{65} +(-4.23760e7 + 1.14111e7i) q^{66} +(1.38518e7 + 4.50073e6i) q^{67} +(1.05578e7 + 9.45892e6i) q^{68} +(251083. - 772754. i) q^{69} +(-2.98289e7 - 2.88334e7i) q^{70} +(3.43784e7 - 1.11702e7i) q^{71} +(2.86590e7 - 2.88734e7i) q^{72} +(3.57169e6 + 2.59498e6i) q^{73} +(2.14603e7 + 8.20727e6i) q^{74} +(3.62067e7 - 3.47235e7i) q^{75} +(3.32909e7 - 3.71585e7i) q^{76} +(7.16827e7 + 5.20805e7i) q^{77} +(-7.43477e7 - 3.80378e6i) q^{78} +(-2.97007e7 + 9.65034e6i) q^{79} +(2.33848e7 - 3.36285e7i) q^{80} +(-2.95565e6 + 9.09657e6i) q^{81} +(1.79184e7 + 6.85271e6i) q^{82} +(-1.76996e7 - 5.75094e6i) q^{83} +(-1.35683e8 - 1.39200e7i) q^{84} +(3.44707e7 + 3.07578e6i) q^{85} +(-7.68207e7 + 5.00238e7i) q^{86} +(2.25397e7 + 3.10232e7i) q^{87} +(-3.94244e7 + 7.80930e7i) q^{88} +(4.01599e7 + 2.91778e7i) q^{89} +(1.38704e7 - 9.83476e7i) q^{90} +(8.83465e7 + 1.21598e8i) q^{91} +(-813313. - 1.40065e6i) q^{92} +1.14224e8 q^{93} +(-4.68207e6 - 3.78184e6i) q^{94} +(1.08253e7 - 1.21320e8i) q^{95} +(-7.88295e6 - 1.34433e8i) q^{96} +(-1.94250e7 - 5.97840e7i) q^{97} +(9.99378e7 + 1.53473e8i) q^{98} +2.12125e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 464 q + 29 q^{2} + 509 q^{4} - 1230 q^{5} - 515 q^{6} + 21284 q^{8} + 262434 q^{9} + 3445 q^{10} - 35805 q^{12} - 29522 q^{13} - 33705 q^{14} - 63391 q^{16} - 319922 q^{17} - 569696 q^{18} + 1244935 q^{20}+ \cdots + 209675864 q^{98}+O(q^{100}) \) 464 * q + 29 * q^2 + 509 * q^4 - 1230 * q^5 - 515 * q^6 + 21284 * q^8 + 262434 * q^9 + 3445 * q^10 - 35805 * q^12 - 29522 * q^13 - 33705 * q^14 - 63391 * q^16 - 319922 * q^17 - 569696 * q^18 + 1244935 * q^20 + 39360 * q^21 + 140220 * q^22 + 989900 * q^24 - 431710 * q^25 - 855842 * q^26 - 2358605 * q^28 - 2884562 * q^29 + 7229675 * q^30 - 7078666 * q^32 - 1866570 * q^33 + 1448973 * q^34 + 777029 * q^36 - 7317972 * q^37 + 4012465 * q^38 - 4154830 * q^40 + 1687438 * q^41 - 21337315 * q^42 + 510580 * q^44 + 2596050 * q^45 + 1721385 * q^46 + 41153690 * q^48 - 396068336 * q^49 - 60015715 * q^50 - 8419912 * q^52 + 26717388 * q^53 - 13729145 * q^54 + 7138890 * q^56 - 19745300 * q^57 - 41444182 * q^58 + 96768050 * q^60 + 26136558 * q^61 - 87505940 * q^62 + 19616924 * q^64 + 22030140 * q^65 - 69968200 * q^66 + 276958 * q^68 - 73697610 * q^69 + 39639840 * q^70 - 145994351 * q^72 - 39004722 * q^73 + 4922908 * q^74 - 19181080 * q^76 + 111211200 * q^77 - 197089615 * q^78 - 395680960 * q^80 - 539852286 * q^81 + 186999258 * q^82 - 377672700 * q^84 - 283475540 * q^85 - 340843785 * q^86 - 29231040 * q^88 - 206040612 * q^89 + 351285695 * q^90 + 43044280 * q^92 + 241823660 * q^93 - 442380075 * q^94 - 474931550 * q^96 + 2388718 * q^97 + 209675864 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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